Communicating an identity of a group shared secret to a server

ABSTRACT

An identity is communicated by a client device to a server without requiring the identity to be disclosed to eavesdroppers and without requiring the use of symmetric or asymmetric cryptography. In one example, the identity is an identity of the client device, where the identity has been assigned to the client device by the server through the provisioning of a unique subset of client-identifying keys. In another example, the identity is an identity of a group shared secret that has been provisioned by the server to the client device.

TECHNICAL FIELD

The technology described herein relates generally to identityprotection.

BACKGROUND

A client device may seek to communicate an identity to a server. Forexample, prior to permitting a client device to gain access to one ormore services in a network, a server of the network may requireauthentication of the client device as proof that the client device is alegitimate client of the network server. In order to authenticate itselfto the server, the client device may be required to communicate anidentity to the server.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a first technique for theprovisioning of client-identifying keys by a server to a plurality ofclient devices, and the communication of one client device's provisionedclient-identifying key to the server;

FIG. 2 is a schematic diagram illustrating a second technique for theprovisioning of client-identifying keys by a server to a plurality ofclient devices, and the communication of one client device's provisionedclient-identifying keys to the server;

FIG. 3 is a flowchart illustrating an example method to be performed bya provisioning server for provisioning client-identifying keys to clientdevices;

FIG. 4 is a flowchart illustrating an example method to be performed bya provisioned client device for communicating its provisionedclient-identifying keys to a receiving server;

FIGS. 5-1 and 5-2 are flowcharts illustrating an example method to beperformed by a receiving server for determining whether a receivedmessage could have been communicated by a client device that wasprovisioned with one or more client-identifying keys;

FIG. 6 is a schematic diagram illustrating a first example technique forthe provisioning of group shared secrets by a server to a plurality ofclient devices, and the communicating of one client device's provisionedgroup shared secret to the server;

FIG. 7 is a flowchart illustrating a first example method to beperformed by a provisioning server for provisioning group shared secretidentifying keys to client devices;

FIG. 8 is a flowchart illustrating a first example method to beperformed by a provisioned client device for communicating one of itsprovisioned group shared secrets to a receiving server;

FIGS. 9-1 and 9-2 are flowcharts illustrating a first example method tobe performed by a receiving server for determining whether a receivedmessage from a client device identifies a group shared secret andwhether the client device possesses the identified group shared secret;

FIG. 10 is a schematic diagram illustrating a second example techniquefor the provisioning of group shared secrets by a server to a pluralityof client devices, and the communicating of one client device'sprovisioned group shared secret to the server;

FIG. 11 is a flowchart illustrating a second example method to beperformed by a provisioning server for provisioning group shared secretidentifying keys to client devices;

FIG. 12 is a flowchart illustrating a second example method to beperformed by a provisioned client device for communicating one of itsprovisioned group shared secrets to a receiving server;

FIGS. 13-1 and 13-2 are flowcharts illustrating a second example methodto be performed by a receiving server for determining whether a receivedmessage from a client device identifies a group shared secret andwhether the client device possesses the identified group shared secret;

FIG. 14 is a flowchart illustrating an example method to be performed bya server for identification and authentication of a client device;

FIG. 15 is a block diagram of an example provisioning server, an exampleclient device, and an example server configured to perform the techniqueillustrated in FIG. 2;

FIG. 16 is a block diagram of an example provisioning server, an exampleclient device, and an example server configured to perform the techniqueillustrated in FIG. 6; and

FIG. 17 is a block diagram of an example provisioning server, an exampleclient device, and an example server configured to perform the techniqueillustrated in FIG. 10.

DETAILED DESCRIPTION

The examples described herein are illustrated primarily in relation toone or more servers and one or more client devices. Each server maycomprise one or more servers, databases, computing devices,communication devices, or other computing equipment adapted tocommunicate over a network (either fixed or wireless) with clientdevices. Client devices may comprise servers, personal computers, orother data processing or communication devices, such as wirelesscommunication devices, communicating over fixed and wireless networksand public networks.

It will be appreciated by those skilled in the art, however, that thisdescription is not intended to limit the scope of the described examplesto implementation on these particular systems or devices. For example,the methods and systems described herein may be applied to anyappropriate communication device or data processing device adapted tocommunicate with another communication or data processing device over afixed or wireless connection, whether portable or wirelessly enabled ornot, whether provided with voice communication capabilities or not, andadditionally or alternatively adapted to process data and carry outoperations on data in response to user commands for any number ofpurposes, including productivity and entertainment.

Thus, the examples described herein may be implemented on computingdevices adapted for communication or messaging, including withoutlimitation cellular phones, smartphones, wireless organizers, personaldigital assistants, desktop computers, terminals, laptops, tablets,handheld wireless communication devices, notebook computers,entertainment devices such as MP3 or video players, and the like. Unlessexpressly stated, a client, computing or communication device mayinclude any such device, and a server may include similar types ofdevices, configured to provide some or all of the processes describedherein. The configuration and operation of all such devices generallywill be known to those skilled in the art. The devices described hereinmay be configured to manage cryptographic keys. For example, any of thedevices described herein may comprise or be configured to operate inconjunction with one or more key management components, including, forexample, a Subscriber Identity Module (SIM) card, a smart card, atrusted platform module (TPM), or a hardware security module (HSM).

A client device may seek to provide an identity, and optionally someproof of the identity to a network server. This may happen, for example,as part of the process of the client device authenticating itself to thenetwork server. As another example, in the case that the client deviceis a satellite telephone with limited coverage, it may provide theidentity to a server as part of a check-in process to determine if ithas any pending text messages for download. In yet another example, inthe case that the client device is a cellular telephone, it may providethe identity to a server when periodically announcing its presence in anarea. The identity being provided by the client device may be, forexample, an identity of the client device, an identity of a SIM card, anidentity of a group to which the client device belongs, or an identityof a group shared secret held by the client device. It may be ofinterest to ensure that the identity is communicated by the clientdevice to the server in such a way that the identity cannot beunderstood by an eavesdropper. It may also be of interest to ensure thatthe client device cannot be tracked by an eavesdropper as a result ofcommunicating the identity. It may be possible for a client device toobscure the identity it is communicating to the server by usingtraditional cryptographic techniques, such as asymmetric cryptography,or by using database lookups, such that each time the client device andthe server communicate in secret, they agree on a new random identifierto be used during the next communication. However, these techniques maybe computationally expensive when a Denial of Service (DoS) attack or asimilar increase in computational load is being experienced. From thepoint of view of the server, part of the DoS risk is related to the factthat the server is not privy to an identity of the purported clientdevice with which the server is communicating. Without being privy tothis identity, the server may be unable to screen out a purported clientdevice which is behaving maliciously.

A technique is herein proposed whereby a client device that haspreviously been provisioned with one or more cryptographic keys by aprovisioning server is able to communicate an identity to a server,herein described as a “receiving” server. The provisioned keys have beenselected from a plurality of cryptographic keys and embedded in theclient device at the time of manufacture, or provisioned at a laterdate, for example, via a storage module like a SIM or over a securechannel. The receiving server may have access to the set ofcryptographic keys or to data dependent on the cryptographic keys, aswell as access to information from which it is determinable which of thecryptographic keys were provisioned to the client device. The clientdevice is able to use one or more of its provisioned keys to communicatean identity to the receiving server. Examples of possible identitiesthat may be communicated by the client device include an identity of theclient device itself, an identity of a SIM card associated with theclient device, an identity of a group to which the client devicebelongs, an identity of a group shared secret held by the client device,or any other identity.

The basic principles of an example technique for communicating anidentity from a client device to a server are described with respect toFIG. 1, which illustrates a server 104 and a plurality of client devices100, including a client device 101, a client device 102 and a clientdevice 103. The client devices 100 are illustrated as wirelesscommunication devices, however, any of the client devices 100 mayalternatively or additionally communicate via one or more fixedconnections. Properties of the client devices 100 and the server 104will be discussed later, with respect to FIGS. 15-17. In this simpleexample, the server 104 may store or have access to a plurality ofcryptographic keys 106, which will herein be referred to asclient-identifying keys 106 for reasons that will become apparent later.The client-identifying keys 106, which include key k₁ 108, key k₂ 110and key k₃ 112, may be identified by indices 114, namely, index 1, index2, and index 3, as shown in FIG. 1. In another example (not shown), theclient-identifying keys 106 may be identified by arbitrary identifiers.In yet another example (not shown), the client identifying keys mayeffectively identify themselves.

Each one of the client-identifying keys 106 is a distinct value. In oneexample, each of the client-identifying keys 106 is an effectivelyrandom value, such that it cannot be generated again on anotheroccasion, except by chance. In this case, the client-identifying keys106 would be stored by the server 104 for future reference, for example,in a lookup table. In another example, each of the client-identifyingkeys 106 is a quasi-random or pseudo-random value generated using anysuitable generation algorithm, such that the same client-identifying key106 can be reliably generated on another occasion in a repeatablemanner. For example, a particular client-identifying key k_(i) could becalculated as a hash of a concatenation of a random seed value s and anindex i, that is k_(i)=h(s|i), where h is any suitable hash algorithm,such as SHA-1, SHA-2, or MD5. In this case, the client-identifying keys106 may not be stored by the server 104, provided that the server 104maintains a record of the conditions under which the client-identifyingkeys 106 were generated, including, for example, the hash algorithm hand the random seed value s. Each one of the client-identifying keys 106may be of a sufficient length and complexity that it cannot be easilypredicted or guessed by an attacker.

The server 104 assigns and provisions the client-identifying keys k₁108, k₂ 110 and k₃ 112 to the client devices 101, 102 and 103,respectively. The client-identifying keys k₁ 108, k₂ 110 and k₃ 112 maybe embedded in the client devices 101, 102 and 103, respectively, at thetime of manufacture, or provisioned at a later date, for example, via astorage module such as a SIM, or via a transmission over a securechannel.

The assignment of the client-identifying keys 106 to client devices maybe carried out in a random, pseudo-random or quasi-random fashion or maybe carried out in an arbitrary fashion, and the server 104 may maintaina record (not shown) of which of the client-identifying keys 106 wasassigned to which client device, for example, in the form of a mappingfunction or a lookup table. Alternatively, the assignment of theclient-identifying keys 106 to client devices may be carried outaccording to an algorithm. In either case, the server 104 may storeinformation (not shown) from which it is determinable which of theclient-identifying keys 106 was provisioned to which client device.Thus, the information may comprise the relevant mapping function, lookuptable, algorithm or inverse thereof, or any other information by whichthe server 104 can determine which of the client-identifying keys 106was provisioned to which client device, or can determine to which clientdevice the subset of client-identifying keys 106 were assigned.

Alternatively, even if, at the time of assigning the client-identifyingkeys 106 to the client devices, the server 104 does not maintain anyinformation from which it is determinable which of theclient-identifying keys 106 was provisioned to which client device, itmay still be possible for the server 104 to subsequently obtain suchinformation. For example, after being provisioned with their respectiveclient-identifying keys, the client devices could subsequently inform acentral infrastructure of which of the client-identifying keys theypossess, thereby permitting the server 104 to reconstruct a mappingfunction. For example, client devices that were provisionedclient-identifying keys during manufacture could subsequently registerthemselves with a central infrastructure when first activated, andsimultaneously provide indications of the client-identifying keys withwhich they were provisioned. In this case, it will be apparent to thoseof ordinary skill in the art that it may be of interest to communicatesuch indications over a secure channel.

Returning to FIG. 1, the server 104 may possess a modulating value Tthat changes from time to time and is agreed on by the server 104 andany provisioned client devices. For example, the modulating value T maybe a time interval value T and may be defined as the whole number offixed-length intervals (or variable-length intervals) since somearbitrary point in time. For ease of understanding, the modulating valueT is described herein as the time interval value T. However, it will beappreciated that the value T may refer to any modulating value thatchanges from time to time.

The time interval value T may be updated by the server 104 and anyprovisioned client devices according to one or more clocks, which may besynchronized. Alternatively or additionally, the server 104 maybroadcast a current time interval value T to any provisioned clientdevices. The provisioned client devices may check that a current timeinterval value T has not been previously used.

It is possible that the time interval value T may be based on a spatiallocation. For example, in the case of wireless hotspots in coffee shops,each coffee shop may have its own server, and each server might have itsown time interval value T.

It is also possible that the time interval value T may be determinedaccording to a combination of a time on a clock and a spatial location.For example, the time interval value T may determined by “outputconcatenation/Cartesian product”.

At any given moment in time, a legitimate client device may possess acurrent time interval value T that differs from a current time intervalvalue T possessed by the server 104. The current time interval value Tof the legitimate client device may differ from that of the server 104,for example, due to clock disagreement or latency associated withbroadcasting or synchronization.

For each new time interval value T and for each of theclient-identifying keys 106, the server 104 may apply a function H to acombination of the time interval value T and the client-identifying key.Such a combination of two or more values, for example value X and valueY, is denoted herein as (X|Y) and refers to a concatenation or to anyother combination of the values. The function H may be a function thatis difficult to reverse, such as a hash algorithm. For example, thefunction H may be any of SHA-1, SHA-2, or MD5. In one example, thefunction H is a SHA-2 algorithm no smaller than SHA-256. It will beappreciated, however, that the function H may represent otheroperations. For example, the function H may correspond to a blockcipher. It will also be appreciated that the definition of the functionH may change from time to time, provided that the definition is agreedon by the entities involved, in this case, the server 104 and the clientdevices 101, 102 and 103. For example, the definition of the function Hmay change in accordance with a change in the current time intervalvalue T. The server 104 may broadcast an indication of the function Hthat is currently in use. For simplicity, in the following discussion,the function H is referred to as a hash algorithm H, and any expressionof the form H(X) is described as a hash.

It is noted that the length of time over which a particular timeinterval value T remains unchanged should generally be sufficient toallow the server 104 to calculate and store any required hashes for anytime interval value T that is likely to be considered current by aprovisioned client device, as will be discussed further below. Forexample, the shorter the length of the time interval, the more intervalsthe server 104 may need to consider active at any given time, dependingon a maximum acceptable clock differential between the client devicesand the server 104. However, as will be discussed later, it is still ofinterest to keep the length of the time interval short enough to limitthe window of opportunity for replay attacks, and to reduce the risk ofbeing tracked by an eavesdropper. In one example, the length of any timeinterval is between five minutes and twenty minutes.

In the example of FIG. 1, the server 104 uses the hash algorithm H tocompute hashes H(T|k₁) 118, H(T|k₂) 120 and H(T|k₃) 122. The server 104may store each of the hashes H(T|k₁) 118, H(T|k₂) 120 and H(T|k₃) 122 ina table 116. Alternatively, the server 104 may store only a portion ofeach of the hashes H(T|k₁) 118, H(T|k₂) 120 and H(T|k₃) 122 in the table116. In one example, the server 104 may only store enough of each one ofthe hashes H(T|k₁) 118, H(T|k₂) 120, and H(T|k₃) 122 to distinguish thestored value from the rest of the values stored in the table 116. Forexample, for a hash that is 256 bits in length, it may be sufficient tostore only the first 128 bits or the last 128 bits or any predetermined128 bits of the hash in order for the stored value to be distinguishedfrom rest of the values stored in the table 116. In another example, aprefix tree, also known as a trie, could be used to preserve some numberof bits at the beginning of each hash, where the number of bitspreserved is the smallest number which distinguishes that value from allother values in the trie. For example, if there are one million hashes,but only one of the hashes has a zero as its first bit, only a singlebit of that hash would be preserved in the trie. In this case, thenumber of bits stored for each hash may vary from hash to hash. Inanother example, a variation of trie could be used in which a specificbit is compared at each step, such that different bits are preserved fordifferent values. In yet another example, for each of the hashes H(T|k₁)118, H(T|k₂) 120 and H(T|k₃) 122, the server 104 may compute some othervalue dependent thereon, and store the hash-dependent values in thetable 116. For example, each hash-dependent value may be computed byapplying a hash algorithm F to a combination of one of the hashesH(T|k_(i)) and a small random seed value s, that is F(H(T|k_(i))|s),where the hash algorithm F may be the same or different from the hashalgorithm H, where the seed value s is determined by trial and errorsuch that the first N bits of each hash-dependent value F(H(T|k_(i))|s)are unique amongst all the hash-dependent values, and where N may beclose to the theoretical limit on size (i.e., the minimum number of bitsfor which the new hashes can still be distinguished from each other).

Thus, while table 116 is illustrated as comprising each of the hashesH(T|k₁) 118, H(T|k₂) 120 and H(T|k₃) 122 in its entirety, the table 116should be understood as alternatively comprising only a portion of eachof the hashes H(T|k₁) 118, H(T|k₂) 120 and H(T|k₃) 122, or,alternatively, values dependent thereon.

In addition, the combination of elements to which the hash algorithm His applied may comprise additional elements (not shown) beyond a timeinterval value T and a particular client-identifying key k_(i). Forexample, the combination may comprise the index i of theclient-identifying key k_(i), such that the hash corresponding to theparticular client-identifying key k_(i) is expressed as H(T|i|k_(i)).Including an index as salt in a hash calculation may make the hash valueharder to attack.

In any case, since each of the values stored in the table 116 may becomputed as a result of applying a hash algorithm H to a combinationthat includes at least the time interval value T and a particularclient-identifying key k_(i), for simplicity, these values will hereinbe referred to as hash-dependent values, and any table in which thesevalues are stored will herein be referred to as a table ofhash-dependent values. However, it will be appreciated that a table isonly one way in which the hash-dependent values may be stored, and thatother data structures are possible for storage of the hash-dependentvalues.

In order to account for client devices that possess adjacent timeinterval values T due, for example, to clock disagreement or latency asdiscussed previously, the server 104 may maintain one or more additionaltables of hash-dependent values (not shown) determined from previoustime interval values T or future time interval values T or both.Alternatively, the server 104 may maintain a single table that includeshash-dependent values determined from the present time interval value Tand from previous time interval values T or future time interval valuesT or both. For example, if the time interval value T changes once perhour, the server 104 may store the hash-dependent values correspondingto the time interval value T for the current hour and either theprevious hour or the next hour, or both.

For each table of hash-dependent values, the server 104 may associateeach one of the hash-dependent values in the table with the respectiveone of the client-identifying key 106 from which the hash-dependentvalue was determined (or with the respective one of the indices 114 ofthe client-identifying key 106 from which the hash-dependent value wasdetermined). The association may comprise, for example, a reverse map, ahash table, an index tree, an exhaustive linear search, or an ad-hocfunction f.

In the case that the association comprises a hash table, some of theinformation about a hash-dependent value may be probabilisticallypreserved. For example, the position of a record in the hash table maydepend on the hash-dependent value itself, but the position of therecord may not be completely deterministic in isolation. For example,the location of other records in the hash table may force a particularrecord to be relocated. It is possible that one portion of ahash-dependent value could be used to determine storage location, whileanother portion could be used for comparison with a hash-dependent valuereceived from a client device, as will be discussed later.

In the case that the association comprises an ad-hoc function f thatassociates a particular hash H(T|k_(i)) to a particularclient-identifying key k_(i), the function might be defined as f:H(T|k_(i))→k_(i) for valid time interval values T and validclient-identifying keys k_(i). It will be appreciated that, for invalidtime interval values T and/or invalid client-identifying keys k_(i), thefunction f need not satisfy any particular requirements. In the exampleof FIG. 1, the association (not shown) for the table 116 ofhash-dependent values would associate the hashes H(T|k₁) 118, H(T|k₂)120, and H(T|k₃) 122 to the client-identifying keys k₁ 108, k₂ 110 andk₃ 112, respectively (or to index 1, index 2, and index 3,respectively).

At any time after being provisioned with its respectiveclient-identifying key, any of the client devices 101, 102 or 103 mayseek to communicate an identity to the server 104. For example, a clientdevice may be required to provide an identity as a prerequisite toauthentication with the server 104, or as part of a check-in processwith the server 104. In another example, the client device may seek toprovide an identity when periodically announcing its presence to theserver 104.

In the example illustrated in FIG. 1, the client device 103 seeks tocommunicate an identity to the server 104. For simplicity, it may beassumed that the identity is an identity of the client device 103,however, the identity could be some other identity, such as an identityof a SIM card of the client device 103.

In the simplified example of FIG. 1, the identity of the client device103 may be communicated to the server 104 using the client-identifyingkey k₃ 112 that the client device 103 received from the server 104.Rather than sending the client-identifying key k₃ 112 directly to theserver 104, the client device 103 may apply the hash algorithm H to acombination of at least the current time interval value T and theclient-identifying key k₃ 112, thereby obtaining a hash H(T|k₃) 124. Thenature of the combination and the definition of the hash algorithm H arethe same as that used by the server 104 to calculate the hashes H(T|k₁)118, H(T|k₂) 120 and H(T|k₃) 122 as described previously. The clientdevice 103 may communicate the hash H(T|k₃) 124 to the server 104, andthe server 104 may proceed to compare the hash H(T|k₃) 124 or a portionthereof or a value dependent thereon to the hash-dependent values in thetable 116. In addition, the server 104 may optionally compare the hashH(T|k₃) 124 or a portion thereof or a value dependent thereon tohash-dependent values stored in one or more additional tables (notshown) corresponding to one or more adjacent time interval values T.This may be done until the server 104 locates a hash-dependent valuethat is consistent with the hash H(T|k₃) 124 or a corresponding portionthereof or a value dependent thereon. For example, upon comparing thehash H(T|k₃) 124 to the hash H(T|k₁) 118, the server 104 will determinethat the hashes are not consistent. The server 104 may proceed tocompare the hash H(T|k₃) 124 to the hash H(T|k₂) 120. Upon determiningthat the hash H(T|k₃) 124 is not consistent with the hash H(T|k₂) 120,the server 104 may then compare the hash H(T|k₃) 124 to the hash H(T|k₃)122. Upon determining that the hash H(T|k₃) 124 is consistent with thehash H(T|k₃) 122, the server 104 may cease to do any more comparisons.

In another example, in the case that the table 116 stores hash-dependentvalues, such as F(H(T|k_(i))|s), as described previously, where s is aseed value determined by trial and error and F is a hash algorithm thatis the same as or different than the hash algorithm H, upon receipt ofthe hash H(T|k₃) 124 from the client device 103, the server 104 maycompute a corresponding hash-dependent value F(H(T|k₃)|s) for comparisonwith the hash-dependent values F(H(T|k_(i))|s) stored in the table 116.It will be appreciated that, in this case, there will be no directcomparison between any portion of the hashes H(T|k₁) 118, H(T|k₂) 120,and H(T|k₃) 122 and any portion of the hash H(T|k₃) 124.

In the case that only a portion of the hash H(T|k₃) 124 or a valuedependent thereon is used by the server 104 for comparison to portionsof hashes or hash-dependent values stored tables of hash-dependentvalues, the client device 103 may only communicate the relevant portionof the hash H(T|k₃) 124 or the relevant hash-dependent value to theserver 104. In this case, the portion of a particular hash H(T|k_(i))that is needed for comparison or the manner by which the hash-dependentvalue is to be determined may be broadcasted or otherwise communicatedto the client device 103 by the server 104. However, given thatbandwidth may be inexpensive, it may be unnecessary to strictly limitthe size of the portion of a particular hash H(T|k_(i)) that iscommunicated to the server 104. It is noted that, unlike the clientdevices 100, the server 104 may store the hash-dependent values for allprovisioned client devices, and may therefore be in a position to checkfor collisions and resolve them using a secondary strategy, such as amodestly-sized secondary table to distinguish between hash-dependentvalues.

Returning to FIG. 1, once the server 104 locates one of the storedhash-dependent values that is consistent with the received hash H(T|k₃)124 or portion thereof or value dependent thereon, the server 104 mayuse the association to determine which one of the client-identifyingkeys 106 (or the indices 114) is associated with the consistenthash-dependent value. In this case, since the stored hash H(T|k₃) 122 isconsistent with the received hash H(T|k₃) 124, the server 104 mayproceed to use the association to determine that the hash H(T|k₃) 122 isassociated with the client-identifying key k₃ 112 (or with the index 3).Now the server 104 may use the stored information (not shown) from whichit is determinable which of the client-identifying keys 106 was assignedto which client device in order to determine which client device, ifany, was provisioned with the client-identifying key k₃ 112 (or with thekey having the index 3). In this case, the server 104 determines that itwas the client device 103 that was provisioned with theclient-identifying key k₃ 112.

In this example, no two client devices were provisioned with the sameone of the client-identifying keys 106, and thus the client-identifyingkey k₃ 112 is unique to the client device 103. It follows that theclient device 103 may use the client-identifying key k₃ 112 to uniquelyidentify itself to the server, and it may do so in a way that cannot beunderstood by an eavesdropper. Furthermore, since the client device 103is communicating a value that changes with each new time interval valueT, it is not possible for the client device 103 to be tracked by aneavesdropper from one time interval value T to the next. Theeavesdropper cannot predict which hash-dependent value will becommunicated by the client device 103 during a future time intervalvalue T.

As mentioned previously, the client device 103 may be susceptible totracking by an eavesdropper during the period when the time intervalvalue T remains unchanged. For this reason, it may be of interest to useshort-length time interval values or to provision each client devicewith multiple sets of client-identifying keys, or both.

As also mentioned previously, the proposed technique is not resistant toreplay attacks during the period when the time interval value T remainsunchanged. For example, an eavesdropper could overhear the hash H(T|k₃)124 that the client device 103 communicates to the server 104. Eventhough the eavesdropper does not know the client-identifying key k₃ 112from which the hash H(T|k₃) 124 was calculated, if the eavesdropperrepeats the hash H(T|k₃) 124 to the server 104 before the time intervalvalue T has changed, the eavesdropper will effectively be communicatingthe identity of the client device 103 to the server 104, even though itis not the client device 103. The eavesdropper may not even be aware ofwhich client device it is purporting to be. Thus, the server 104 canonly use a received hash to determine if the hash could have beencommunicated by a client device that was provisioned with one of theclient-identifying keys 106. For example, if the server 104 receives amessage comprising a value that is not consistent with any of thehash-dependent values in the table 116 or in any other table ofhash-dependent values (not shown), the server 104 can determine withcertainty that the message does not identify a client device that wasprovisioned with one of the client-identifying keys 106. Similarly, evenif the value is consistent with one of the hash-dependent values in thetable 116 or in any other table of hash-dependent values (not shown),but the consistent hash-dependent value is associated with aclient-identifying key that was not provisioned to any client device,the server 104 can also determine with certainty that the message doesnot identify a client device that was provisioned with one of theclient-identifying keys 106. However, if the server 104 receives amessage comprising a value that is consistent with one of thehash-dependent values in the table 116 or in any other table ofhash-dependent values (not shown), and the consistent hash-dependentvalue does correspond to one of the client-identifying keys 106 that wasprovisioned to a particular client device, the server 104 can onlydetermine that the message identifies that particular client device, andtherefore could have been communicated by that particular client device.In other words, for a received message that includes a hash or portionthereof or value dependent thereon, the server 104 can either determinean identity of a single client device which could have legitimately sentthe message, or determine that no legitimate client device could havesent the message. It is noted that, while it is theoretically possiblefor a hash of one value to be the same as the hash of another differentvalue, it is astronomically unlikely.

It is also noted that, in the case that an attacker repeatedly prompts aclient device to disclose an identity, it is possible that the attackercould measure the exact moment that the time interval value T of theclient device changes, thereby permitting the attacker to track theclient device in the future based on any discrepancy in the clientdevice's clock. For example, the attacker might be able to track aparticular client device based on that client device's clock being 12.6seconds fast. This risk may be mitigated by having the client devicesobtain the current time interval value T from the server 104, by havingthe client devices regularly synchronize their clocks with a centralauthority, or by introducing a small random element into the timing ofeach client device, such that clock discrepancies between client devicescannot be accurately measured by an attacker.

For a server with a very large number of client devices, the simplifiedtechnique illustrated in FIG. 1 may impose a large computational burden.For example, if the server had to communicate with one hundred millionclient devices, the server would have to store at least one hundredmillion client-identifying keys in order for each client device to beprovisioned with a unique client-identifying key. The server would alsohave to compute one-hundred million hashes at every new time intervalvalue T, which might be unfeasible. It might also be unfeasible for theserver to compare a received hash or portion thereof with one hundredmillion hashes or portions thereof. Although a high-end server might beable to handle such a load given a modestly-optimized implementation,power usage, key security and latency would suffer significantly.Furthermore, with a minimum of 3200 MB of key material (based on 128-bitkeys), key management would pose a significant challenge.

The computational burden on the server could be reduced by provisioningmore than one client-identifying key to each client device. For example,if the server were to store N client-identifying keys, and to provisioneach client device with a unique subset of Y of the N client-identifyingkeys, according to the equation for the binomial coefficient C(N, Y)with the number N of client-identifying keys being much larger than thenumber Y of client-identifying keys in the subset, the server would beable to uniquely provision approximately N^(Y)/Y! client devices, where“Y!” denotes the factorial of the number Y. In one example, if theserver stores N=1,000,000 client-identifying keys, and each clientdevice is provisioned with a unique subset of Y=4 of the 1,000,000client-identifying keys, the server would be able to uniquely provisionapproximately 4.17×10²² client devices. Thus, by provisioning eachclient device with more than one client-identifying key, the techniquedescribed with respect to FIG. 1 may be scaled for use with a muchlarger number of client devices. The size of the subset ofclient-identifying keys provisioned may vary from one client device toanother.

Accordingly, FIG. 2 is a schematic diagram illustrating a second exampletechnique for the provisioning of client-identifying keys by a server200 to a plurality of client devices 101, 102 and 103, and thecommunication of the client device 103's provisioned client-identifyingkeys to the server 200. In contrast to the example technique illustratedin FIG. 1, the example technique illustrated in FIG. 2 involves theprovisioning of a plurality of client-identifying keys to each one ofthe client devices 101, 102 and 103.

The server 200 may store or have access to N client-identifying keys(k₁, k₂, k₃, . . . , k_(N)) 202. The N client-identifying keys 202 maybe identified by N corresponding indices (1, 2, 3, . . . , N) 204, whereN may take on any positive integer value. In another example (notshown), each of the N client-identifying keys 202 may be identified byan arbitrary identifier. In yet another example (not shown), each of theN client-identifying keys 202 may effectively identify itself.Typically, the number N of client-identifying keys 202 will be less thanthe number of client devices that may communicate with the server 200.In one example, the number N of client-identifying keys 202 isN=1,000,000.

Each one of the client-identifying keys 202 is a distinct value. In oneexample, each of the client-identifying keys 202 is an effectivelyrandom value, such that it cannot be generated again on anotheroccasion, except by chance. In this case, the client-identifying keys202 would be stored by the server 200 for future reference, for example,in a lookup table. In another example, each of the client-identifyingkeys 202 is a quasi-random or pseudo-random value generated using anysuitable generation algorithm, such that the same client-identifying key202 can be reliably generated on another occasion in a repeatablemanner. For example, a particular client-identifying key k_(i) could becalculated as a hash of a concatenation of a random seed value s and anindex i, that is k_(i)=h(s|i), where h is any suitable hash algorithm,such as SHA-1, SHA-2, or MD5. In this case, the client-identifying keys202 may not be stored by the server 200, provided that the server 200maintains a record of the conditions under which the client-identifyingkeys 202 were generated, including, for example, the hash algorithm hand the random seed value s. Each one of the client-identifying keys 202may be of a sufficient length and complexity that it cannot be easilypredicted or guessed by an attacker.

In the example illustrated in FIG. 2, the server 200 assigns andprovisions a subset of four of the N client-identifying keys 202 to eachof the client devices 101, 102 and 103. In particular, the server 200assigns a subset 206 of client-identifying keys (k₈, k₁₃, k₂₄, k₆₂) tothe client device 101, a subset 208 of client-identifying keys (k₁, k₂₄,k₃₀, k₅₇) to the client device 102, and a subset 210 ofclient-identifying keys (k₃, k₁₇, k₄₃, k₆₀) to the client device 103.

The subsets 206, 208 and 210 of client-identifying keys may be embeddedin the client devices 101, 102 and 103, respectively, at the time ofmanufacture, or provisioned at a later date, for example, via a storagemodule such as a SIM, or via transmission over a secure channel.

The assignment of a subset of the client-identifying keys 202 to eachclient device may be carried out in a random, pseudo-random orquasi-random fashion or may be carried out in an arbitrary fashion, andthe server 200 may maintain a record (not shown) of which of theclient-identifying keys 202 were provisioned to which client device, forexample, in the form of a mapping function or a lookup table.Alternatively, the assignment of a subset of the client-identifying keys202 to each client device may be carried out according to an algorithm.In either case, the server 200 may store information (not shown) fromwhich it is determinable which of the client-identifying keys 202 wereprovisioned to which client device. Thus, the information may comprisethe relevant mapping function, lookup table, algorithm or inversethereof, or any other information by which the server 200 can determinewhich of the client-identifying keys 202 were provisioned to whichclient device, or can determine to which client device the subset ofclient-identifying keys 202 were assigned.

Alternatively, even if, at the time of assigning the client-identifyingkeys 202 to the client devices, the server 200 does not maintain anyinformation from which it is determinable which of theclient-identifying keys 202 were provisioned to which client device, itmay still be possible for the server 200 to subsequently obtain suchinformation, for example during registration of the provisioned clientdevices with a central infrastructure, as described previously withrespect to FIG. 1.

Since there are likely more client devices than client-identifying keys202, some client devices may share one or more of the sameclient-identifying keys. For example, in FIG. 2, the client devices 101and 102 have each been provisioned with the client-identifying key k₂₄.It is also possible that some of the client-identifying keys 202 may notyet be provisioned to any client device at all, or else that they may beprovisioned to client devices that are not illustrated in FIG. 2. Inthis example, it is assumed that no two client devices are provisionedwith exactly the same subset of client-identifying keys 202.

As described with respect to FIG. 1, the server 200 may possess a timeinterval value T that changes from time to time and is agreed on by theserver 200 and any provisioned client devices. For example, the server200 might broadcast the current time interval value T. For each new timeinterval value T and for each of the client-identifying keys 202, theserver 200 may calculate a hash of a combination of at least the timeinterval value T and the client-identifying key using a hash algorithmH, as described with respect to FIG. 1. In the example illustrated inFIG. 2, the server 200 uses the hash algorithm H to compute hashesH(T|k₁), H(T|k₂), H(T|k₃), . . . , H(T|k_(N)). As described with respectto FIG. 1, the server 200 may store each of the hashes H(T|k₁), H(T|k₂),H(T|k₃), . . . , H(T|k_(N)) in a table 212 or some other suitable datastructure (not shown). Alternatively, the server 200 may store onlyportions of the hashes, or some other values dependent thereon.

As described with respect to FIG. 1, in order to account for clientdevices that possess adjacent time interval values T, the server 200 maymaintain one or more additional tables of hash-dependent values (notshown) determined from previous time interval values T or future timeinterval values T or both. Alternatively, the server 200 may maintain asingle table that includes hash-dependent values determined from thepresent time interval value T and from previous time interval values Tor future time interval values T or both.

For each table of hash-dependent values, the server 200 may associateeach one of the hash-dependent values in the table with the respectiveone of the client-identifying keys 202 from which the hash-dependentvalue was determined (or with the respective one of the indices 204 ofthe client-identifying key 202 from which the hash-dependent value wasdetermined). The association may be implemented as described previouslywith respect to FIG. 1. In the example of FIG. 2, the association (notshown) for the table 212 of hash-dependent values would associate eachone of the hash-dependent values in the table 212 with a correspondingone of the client-identifying keys 202 (or with a corresponding one ofthe indices 204).

The client device 103 may seek to communicate an identity to the server200, where the identity is an identity of the client device 103 or someother identity, such as an identity of a SIM card of the client device103. In the example of FIG. 2, this may be done using theclient-identifying keys (k₃, k₁₇, k₄₃, k₆₀) 210 with which the clientdevice 103 was provisioned by the server 200. For each ofclient-identifying keys (k₃, k₁₇, k₄₃, k₆₀) 210, the client device 103may calculate a hash by applying the hash algorithm H to a combinationof at least the current time interval value T and the client-identifyingkey. The nature of the combination and the definition of the hashalgorithm H are the same as that used by the server 200 to calculate thehashes H(T|k₁), H(T|k₂), H(T|k₃), . . . , H(T|k_(N)) as describedpreviously. From these hash calculations, the client device 103 mayobtain four hashes 214: H(T|k₃), H(T|k₁₇), H(T|k₄₃), and H(T|k₆₀). Theclient device 103 may communicate the hashes 214 to the server 200, and,for each one of the hashes 214, the server 200 may proceed to comparethe hash or a portion thereof or a value dependent thereon to thehash-dependent values H(T|k₁), H(T|k₂), H(T|k₃), . . . , H(T|k_(N))stored in the table 212. In addition, for each one of the hashes 214,the server 200 may optionally compare the hash or a portion thereof or avalue dependent thereon to hash-dependent values stored in one or moreadditional tables (not shown) corresponding to one or more adjacent timeinterval values T. This may be done until the server 200 locateshash-dependent values that are consistent with each of the receivedhashes 214 or corresponding portions thereof or values dependentthereon.

In the case that the table 212 stores hash-dependent values, such asF(H(T|k_(i))|s), as described previously with respect to FIG. 1, uponreceipt of the hashes 214 H(T|k₃), H(T|k₁₇), H(T|k₄₃), and H(T|k₆₀) fromthe client device 103, the server 200 may compute correspondinghash-dependent values F(H(T|k₃)|s), F(H(T|k₁₇)|s), F(H(T|k₄₃)|s), andF(H(T|k₆₀)|s) for comparison with the hash-dependent valuesF(H(T|k_(i))|s) stored in the table 212.

In the case that only a portion of each of the hashes 214 H(T|k₃),H(T|k₁₇), H(T|k₄₃), and H(T|k₆₀) or values dependent thereon are used bythe server 200 for comparison to portions of hashes or hash-dependentvalues stored tables of hash-dependent values, the client device 103 mayonly communicate the relevant portions of the hashes 214 or the relevanthash-dependent values to the server 200. In this case, the portion ofeach hash that is needed for comparison or the manner by which eachhash-dependent value is to be determined may be broadcasted or otherwisecommunicated to the client device 103 by the server 200.

Returning to FIG. 2, once the server 200 locates stored hash-dependentvalues that are consistent with the received hashes 214 or portionsthereof or values dependent thereon, the server 200 may use theassociation to determine which of the client-identifying keys 202 (orthe indices 204) are associated with the consistent hash-dependentvalues. In this case, the server 200 may use the association todetermine that the hash-dependent values that are consistent with thereceived hashes 214 or portions thereof or values dependent thereon areassociated with the client-identifying keys k₃, k₁₇, k₄₃, k₆₀ (or withthe indices 3, 17, 43 and 60). Now the server 200 may use the storedinformation (not shown) from which it is determinable which of theclient-identifying keys 202 were provisioned to which client device inorder to determine which client device, if any, was provisioned with theclient-identifying keys k₃, k₁₇, k₄₃, k₆₀ (or with the keys having theindices 3, 17, 43 and 60). In this case, the server 200 determines thatit was the client device 103 that was provisioned with the subset 210 ofclient-identifying keys (k₃, k₁₇, k₄₃, k₆₀).

In this example, no two client devices were provisioned with exactly thesame subset of the client-identifying keys 202, and thus the subset 210of client-identifying keys (k₃, k₁₇, k₄₃, k₆₀) is unique to the clientdevice 103. It follows that the client device 103 may use theclient-identifying keys (k₃, k₁₇, k₄₃, k₆₀) to uniquely identify itselfto the server 200, and it may do so in a way that cannot be understoodor tracked by an eavesdropper from one time interval value to the next.It will be apparent to those of ordinary skill in the art that, if careis taken in provisioning, it may be possible for a client device touniquely identify itself using only some of the client-identifying keyswith which the client device was provisioned. For example, in thissimple case, it will be apparent that the client device 103 coulduniquely identify itself to the server 200 using any one of its subset210 of client-identifying keys because none of the fourclient-identifying keys in the subset 210 was provisioned to any of theother client devices (i.e., client devices 101 and 102).

Similarly to the technique described with respect to FIG. 1, thistechnique is not resistant to replay attacks during the period when thetime interval value T remains unchanged. For example, an eavesdroppercould overhear the hashes 214 that the client device 103 communicates tothe server 200. Even though the eavesdropper does not know theclient-identifying keys 210 to which the hashes 214 correspond, or thecurrent time interval value T, if the eavesdropper repeats the hashes214 to the server 200 before the time interval value T has changed, theeavesdropper will effectively be communicating the identity of theclient device 103 to the server 200, even though it is not the clientdevice 103. The eavesdropper may not even be aware of which clientdevice it is purporting to be. Thus, the server 200 can only usereceived hash-dependent values to determine if the hash-dependent valuescould have been communicated by a client device that was provisionedwith the subset 210 of client-identifying keys 202. For example, if theserver 200 receives a message comprising values that are not consistentwith any subset of the stored hash-dependent values in the table 212 orin any other table of hash-dependent values (not shown), the server 200can determine with certainty that the message does not identify a clientdevice that was provisioned with a subset of the client-identifying keys202. Similarly, even if the server 200 receives a message comprisingvalues that are consistent with a subset of the stored hash-dependentvalues stored in the table 212 or in another other table ofhash-dependent values (not shown), but the consistent hash-dependentvalues are not associated with any subset of the client-identifying keys202 that was provisioned to a client device, the server 200 candetermine with certainty that the message does not identify a clientdevice that was provisioned with a subset of the client-identifying keys202. However, if the server 200 receives a message comprising valuesthat are consistent with a subset of the hash-dependent values stored inthe table 212 or in any other table of hash-dependent values (notshown), and the consistent hash-dependent values correspond to a subsetof the client-identifying keys 202 that was provisioned to a particularclient device, the server 200 can only determine that the messageidentifies that particular client device, and therefore could have beencommunicated by that particular client device. In other words, for areceived message that includes a subset of hashes or portions thereof orvalues dependent thereon, the server 200 can either determine anidentity of a single client device which could have legitimately sentthe message, or determine that no legitimate client device could havesent the message.

It will be apparent that, in the case that a particular client devicecan be uniquely identified using only some of the client-identifyingkeys with which it was provisioned, as discussed above, the server 200could make this determination when the hash-dependent values received inthe message are consistent with stored hash-dependent values that areassociated with only some of the client-identifying keys of the subsetprovisioned to the particular client device.

While the servers 104 and 200 are each illustrated as a single device,it is contemplated that each of the servers 104 and 200 may comprisemultiple devices. For example, each of the servers 104 and 200 maycomprise one or more provisioning servers, each of which is configuredto provision one or more client-identifying keys to one or more clientdevices. Each of the servers 104 and 200 may also comprise one or morereceiving servers, each of which is able to receive a message purportingto be from a provisioned client device and determine whether the messagecould have been communicated by a provisioned client device. Thecalculation of the hashes and the determination of the hash-dependentvalues to be stored for a particular time interval value T may beperformed by the one or more provisioning servers or by the one or morereceiving servers or by some combination thereof. For example, the oneor more provisioning servers may share information with the one or morereceiving servers, such as any of the client-identifying keys and theinformation from which it is determinable which client-identifying keyswere provisioned to which client device. In one example, the sharedinformation is stored on one or more databases accessible by the one ormore provisioning servers and the one or more receiving servers. Inanother example, in the case of more than one receiving server, eachreceiving server may only be able to identify a subset of the clientdevices that were provisioned by a provisioning server. For example, thereceiving server may not have access to all of the client-identifyingkeys or to the information from which it is determinable whichclient-identifying keys were provisioned to which client device.

In a variation on this system, a given receiving server may not bepermitted or able to identify all client devices that were provisionedby a provisioning server. For example, the receiving server may not haveaccess to all of the client-identifying keys or hashes.

FIG. 3 is a flowchart illustrating an example method to be performed bya provisioning server for provisioning client-identifying keys to clientdevices.

The method begins at 300 by having the provisioning server store or haveaccess to a plurality of N client-identifying keys (k₁, k₂, . . . ,k_(N)). The N client-identifying keys may be identified by indices (1,2, . . . , N), where N may take on any positive integer value.Alternatively, each of the client-identifying keys (k₁, k₂, . . . ,k_(N)) may be identified by an arbitrary identifier or may effectivelyidentify itself. As described with respect to FIG. 2, each one of theclient-identifying keys (k₁, k₂, . . . , k_(N)) is a distinct value,such as an effectively random value, a quasi-random or a pseudo-randomvalue, or a value that can be reliably generated on another occasion ina repeatable manner. In the latter case, it will be appreciated that theserver may not explicitly store the client-identifying keys (k₁, k₂, . .. , k_(N)), provided that the server maintains a record of theconditions under which the client-identifying keys were generated. Eachone of the client-identifying keys (k₁, k₂, . . . , k_(N)) may be of asufficient length and complexity that it cannot be easily predicted orguessed by an attacker.

At 302, the provisioning server assigns to each client device j to beprovisioned a unique subset of M_(j) client-identifying keys (k_(C1),k_(C2), . . . , k_(CMj)) selected from the N client-identifying keys(k₁, k₂, . . . , k_(N)), where M_(j) is a positive integer less than N.In the example illustrated in FIG. 1, the number M_(j) ofclient-identifying keys in the subset for all client devices {j} isM_(j)=1, whereas, in the example illustrated in FIG. 2, the number M_(j)of client-identifying keys in the subset for all client devices {j} isM_(j)=4. In other examples, some of the client devices {j} may have moreclient-identifying keys provisioned thereto than others of the clientdevices {j}. In the present example, all client devices {j} areprovisioned with a subset of M_(j)=M client-identifying keys. Theassignment of the subsets of client-identifying keys to the clientdevices {j} may be carried out in a random, pseudo-random orquasi-random fashion or may be carried out in an arbitrary fashion, andthe server may maintain a record of which of the N client-identifyingkeys (k₁, k₂, . . . , k_(N)) were assigned to which client device j, forexample, in the form of a mapping function or a lookup table.Alternatively, the assignment of the subsets of client-identifying keysto the client devices {j} may be carried out according to an algorithm.As noted previously, two or more client devices may be assigned one ormore of the same client-identifying keys, provided that no two clientdevices are assigned the exact same subset of client-identifying keys(k_(C1), k_(C2), . . . , k_(CM)). It is also possible that some of theclient-identifying keys (k₁, k₂, . . . , k_(N)) may not yet be assignedto any client device at all.

At 304, the provisioning server may store information from which it isdeterminable which M client-identifying keys were assigned to whichclient device. The information may comprise the relevant mappingfunction, lookup table, algorithm or inverse thereof, or any otherinformation by which the server can determine which of theclient-identifying keys were provisioned to which client device. Theprovisioning server may store the information in a memory of theprovisioning server or in one or more databases that are accessible byboth the provisioning server and a receiving server. Alternatively, asdescribed previously, the provisioning server may reconstruct a mappingfunction based on information subsequently obtained from provisionedclient devices.

At 306, the provisioning server provides to each client device to beprovisioned the subset of M client-identifying keys (k_(C1), k_(C2), . .. , k_(CM)) assigned to that client device. Each subset of M assignedkeys (k_(C1), k_(C2), . . . , k_(CM)) may be embedded in a client deviceat the time of manufacture, or provisioned at a later date, for example,via a storage module such as a SIM, or via a transmission over a securechannel.

In the case that the provisioning server reconstructs a mapping functionbased on information subsequently obtained from provisioned clientdevices, it will be appreciated that the provisioning of the clientdevices at 306 may precede the storing of the information at 304.

FIG. 4 is a flowchart illustrating an example method to be performed bya provisioned client device for communicating its provisionedclient-identifying keys to a receiving server.

At 400, the client device receives a unique subset of Mclient-identifying keys (k_(C1), k_(C2), . . . , k_(CM)) from aprovisioning server. As described above, the subset of Mclient-identifying keys may be embedded in the client device at the timeof manufacture, or may be received at a later date.

At some point after being provisioned with its unique subset of Mclient-identifying keys (k_(C1), k_(C2), . . . , k_(CM)), the clientdevice may determine at 402 that it has a need to communicate anidentity to a server. For example, it may seek to request services froma web server which requires identification of the client device as aprerequisite to authentication of the client device.

Once the client device determines at 402 that it has a need tocommunicate an identity to the server, for each of the Mclient-identifying keys received at 400, the client device may proceedat 404 to calculate a hash by applying a hash algorithm H to acombination of at least the current time interval value T and theclient-identifying key, thereby obtaining M hashes: H(T|k_(C1)),H(T|k_(C2)), . . . , H(T|k_(CM)). Although not explicitly shown, theclient device may receive one or more of the current time interval valueT, an indication of the hash algorithm H, and an indication of thenature of the combination via a broadcast from the provisioning serveror a receiving server.

At 406, the client device communicates a message to the servercomprising each of the M hashes H(T|k_(C1)), H(T|k_(C2)), . . . ,H(T|k_(CM)) calculated at 404. Alternatively, for each of the M hashesH(T|k_(C1)), H(T|k_(C2)), . . . , H(T|k_(CM)) calculated at 404, theclient device may communicate a message to the server comprising aportion of each hash or a value dependent thereon.

The methods described herein are based on the assumption that eachclient device is provisioned with the same number M ofclient-identifying keys. However, it will be apparent to a person ofordinary skill in the art that different client devices may beprovisioned with different numbers of client-identifying keys, providedthat no client device is provisioned with a subset of another clientdevice's client-identifying keys. In one example, a client device mayindicate in the message communicated at 406 the number ofclient-identifying keys to which the message pertains.

FIGS. 5-1 and 5-2 are flowcharts illustrating an example method to beperformed by a receiving server for determining whether a receivedmessage identifies a provisioned client device and therefore could havebeen communicated by a client device that was provisioned with one ormore client-identifying keys. The receiving server may be the sameserver as the provisioning server that is configured to perform themethod illustrated in FIG. 3. Alternatively, the receiving server may bea separate server from the provisioning server, but may shareinformation with the provisioning server, including, for example, theplurality of client-identifying keys (k₁, k₂, . . . , k_(N)) and theinformation from which it is determinable which M_(j) client-identifyingkeys were assigned to which client device j. In one example, the sharedinformation is stored on one or more databases accessible by both theprovisioning server and the receiving server.

The example method illustrated in FIG. 5-1 begins at 500 by having theserver store or have access to the N client-identifying keys (k₁, k₂, .. . , k_(N)). The server also stores or has access to the informationfrom which it is determinable which M_(j) client-identifying keys(k_(C1), k_(C2), . . . , k_(CMj)) were assigned to which provisionedclient device j. In this example, all client devices {j} have beenprovisioned with a subset of M_(j)=M client-identifying keys.

At 502, the server calculates for each of the N client-identifying keysa hash of a combination of at least the current time interval value Tand the client-identifying key, thereby obtaining N hashes: H(T|k₁),H(T|k₂), . . . , H(T|k_(N)). The nature of the combination and hashalgorithm H are the same as that used by the client device to calculatehashes at 404.

At 504, the server may store each of the N calculated hashes or portionsthereof or values dependent thereon as hash-dependent values in a tableor some other suitable data structure. Although not shown, the servermay store one or more additional tables of hash-dependent valuesdetermined from previous time interval values T or future time intervalvalues T or both. Alternatively, the server may maintain a single tablethat includes hash-dependent values determined from the present timeinterval value T and from previous time interval values T or future timeinterval values T or both.

At 506, for each table of hash-dependent values, the server associateseach one of the N hash-dependent values in the table with the respectiveone of the client-identifying keys from which the hash-dependent valuewas determined (or with the respective index of the one of the Nclient-identifying keys (k₁, k₂, . . . , k_(N)) from which thehash-dependent value was determined).

At 508, the server checks whether it has received a message purportingto identify a provisioned client device. If the server does not receiveany such message, and if the server determines at 510 that the timeinterval value T has increased, the server proceeds to repeat thecalculation of the N hashes H(T|k₁), H(T|k₂), . . . , H(T|k_(N)) at 502using the new time interval value T. The server may then store newhash-dependent values at 504, and, at 506, associate each one of the newhash-dependent values with the respective one of the Nclient-identifying keys from which the new hash-dependent value wasdetermined (or with the respective index of the one of the Nclient-identifying keys from which the hash-dependent value wasdetermined). As noted above, since the server may store additionalhash-dependent values determined from previous time interval values T orfuture time interval values T or both, the new hash-dependent values mayor may not overwrite previously stored hash-dependent values. Severaltables of hash-dependent values and associations, such as reverse maps,may be maintained at any one time.

Once the server determines at 508 that it has received a messagepurporting to identify a provisioned client device, the server mayproceed to determine at 512 whether the message identifies a provisionedclient device.

The determination made at 512 is described in more detail by the actionsillustrated in FIG. 5-2.

Since, in this example, all legitimate client devices were provisionedwith a subset of M client-identifying keys, the server expects toreceive M components in any message purporting to identify a provisionedclient device. Thus, at 514, the server extracts from the receivedmessage M components purporting to be the hashes H(T|k_(C1)), H(T|k_(C2)), . . . , H(T|k_(CM)) or portions thereof or values dependentthereon. Although not explicitly shown, the server may extract from thereceived message the M components purporting to be the hashesH(T|k_(C1)), H(T|k_(C2)), . . . , H(T|k_(CM)) or portions thereof, andthe server may subsequently calculate values dependent thereon.Extraction of the M components may occur separately for each individualcomponent. Alternatively, in the case that the components have beencombined, for example, using a Bloom filter, extraction of the Mcomponents may be understood as referring to the extraction of thecombination.

At 516, the server compares each extracted component, or relevantportion thereof or value dependent thereon, to each value in the tableof hash-dependent values stored at 504, or optionally to hash-dependentvalues stored in one or more additional tables. This may be done untilthe server locates hash-dependent values that are consistent with eachof the M components extracted at 512.

At 518, the server checks whether there are stored hash-dependent valuesthat are consistent with each of the M extracted components or relevantportions thereof or values dependent thereon. If the server determinesat 518 that one or more of the M components or a relevant portionthereof or value dependent thereon is not consistent with any storedhash-dependent value, the server can determine with certainty at 520that the received message does not identify any provisioned clientdevice.

If the server determines at 518 that each of the M components orrelevant portions thereof or values dependent thereon is consistent witha stored hash-dependent value, the server may proceed to use theassociation at 522 to determine the client-identifying key (or the indexof the client-identifying key) that is associated with each consistenthash-dependent value. At 524, the server may then proceed to use theinformation stored at 500 (i.e., the information from which it isdeterminable which M client-identifying keys were assigned to whichclient device) to determine if the client-identifying keys determined at522 were provisioned to a particular client device.

The server checks at 526 whether the client-identifying keys determinedat 522 correspond to a subset that was provisioned to a particularclient device. If the server determines at 526 that the subset ofclient-identifying keys determined at 522 was not provisioned to anyparticular client device, the server can proceed to determine withcertainty at 520 that the message does not identify any provisionedclient device. This may occur even if each of the M extracted componentscorresponds to a client-identifying key that was provisioned to a clientdevice, but there is no single client device that has been provisionedwith each of the client-identifying keys corresponding to the Mextracted components. For example, with reference to FIG. 2, if aneavesdropping device overhears two of the hashes communicated by theclient device 101 to the server 200, such as the hashes H(T|k₈) andH(T|k₁₃), and the eavesdropping device also overhears two of the hashescommunicated by the client device 102 to the server 200, such as thehashes H(T|k₃₀) and H(T|k₅₇), the eavesdropping device may attempt toidentify itself to the server 200 using a combination of theeavesdropped hashes: H(T|k₈), H(T|k₁₃), H(T|k₃₀), H(T|k₅₇). While theserver 200 would determine at 518 that each of the four components isconsistent with a stored hash value, after using the association at 522and the stored information at 524, the server 200 would determine at 526that the particular subset of client-identifying keys corresponding tothe extracted components was not provisioned to any single clientdevice. Thus, the server 200 would determine with certainty at 520 thatthe message did not identify any provisioned client device. However, itis possible that the combination of the eavesdropped hashes H(T|k₈),H(T|k₁₃), H(T|k₃₀), H(T|k₅₇) could identify another client device notshown in FIG. 2. The larger the number N of client-identifying keys, theless likely it is that that a combination of eavesdropped hashes orhash-dependent values from several client devices would allow aneavesdropper to communicate an identity of another client device.

If the server determines 526 that the subset of client-identifying keysdetermined at 522 was provisioned to a particular client device, theserver may proceed to determine at 528 that the message identifies thatparticular provisioned client device. The server is only able todetermine at 528 that the message could have been communicated by theparticular client device that the message purports to identify. Thesender of the message is communicating a purported identity to theserver, but is not yet proving to the server that it legitimatelypossesses that identity. A client device may prove that it possess theidentity it purports to possess as part of an authentication process.This is described in more detail with respect to FIG. 14.

The proposed technique does not require the use of asymmetriccryptography or the use of symmetric cryptography. The proposedtechnique permits a client device's identity to be communicated in a waythat cannot be understood by eavesdroppers, provided that the hashalgorithm used is irreversible. While an eavesdropper may overhear thehash-dependent values communicated by a particular client device, theeavesdropper cannot determine the client-identifying keys from which thehash-dependent values were calculated, and therefore cannot infer theidentity of the client device. Furthermore, since the hash-dependentvalues communicated by each client device change with each new timeinterval value T, it is not possible for a client device to be trackedby the eavesdropper from one time interval value T to the next. Theeavesdropper cannot predict which hash-dependent values will becommunicated by the client device during a future time interval value T.

An analysis of the performance of the proposed technique is presentedherein using example parameters. In one example, the number N ofclient-identifying keys is N=1,000,000, and each one of theclient-identifying keys is 160 bits in length. The hash algorithm H isSHA-1, which uses 512-bit blocks. This totals 64 MB of material to behashed. According to the crypto++ 5.6.0 benchmarks page(www.cryptopp.com/benchmarks.html), an Intel® Core 2 at 1.83 GHz runninga single core in 32-bit mode can compute a SHA-1 hash at a rate of 153MB/s. This system should be able to complete the required 1,000,000 hashcalculations in about two to three seconds, even with its modest CPU.

The server may build a table of hashes consisting of 2,000,000 32-bitbuckets. The server may use the first 21 bits of a hash as an index intothe table of hashes, and then store the next 12 bits of the hash and a20-bit client-identifying key in the first free bucket. Veryoccasionally, the server will be required to test more than one possibleconsistent client-identifying key. The required storage space for such atable of hashes is approximately 8 MB. The server may be required tostore two such tables of hashes, as the server will have to pre-computethe table of hashes for the next time interval value T before thecurrent time interval ends. Thus, the server will need 16 MB of RAM tostore the hash values and corresponding reverse index. Determining asubset of indices from a subset of hash values received in a message maytake nearly constant time, and may take less time than that required fora single hash calculation. However, this time does not include the timerequired to perform a database lookup if random assignment ofclient-identifying keys were used.

The proposed technique may be used to communicate any identity withoutdisclosing it to eavesdroppers. In one example, the concept may beapplied to the communication of an identity of a group shared secret.

A server may authenticate a client device, for example, using a secretshared between the client device and the server, or a certificate signedby the server. In the case of the shared secret, the server has to spendtime locating the secret in a database in order to authenticate theclient device. In the case of the certificate, the server has to spendtime performing computations in order to authenticate the client device.

When a server is bombarded with authentication requests by illegitimateclient devices, the server's resources may become exhausted and theserver may be unable to authenticate legitimate client devices. This isknown as a Denial of Service (DOS) attack. To address this issue, U.S.patent application Ser. No. 13/083,981 to Suffling, herein incorporatedby reference in its entirety, discloses a method whereby, prior toauthentication, a client device may be pre-authenticated by proving itspossession of a group shared secret that was previously provisioned toone or more legitimate client devices of the network server. Only thoseclient devices that are in possession of the group shared secret may besuccessfully pre-authenticated and permitted to proceed to the moreexpensive step of authentication.

In one example, a provisioning server stores L group shared secrets. Anauthenticating server also maintains the set of L group shared secrets.The provisioning server provisions each client device j with a subset ofP_(j) of the L group shared secrets. When one of the client devicesseeks to authenticate itself to the authenticating server, it transmitsa “pre-authentication” request to the authenticating server based on aselected one of the P_(j) group shared secrets with which it wasprovisioned. The pre-authentication request comprises some proof ofknowledge of the selected group shared secret, such as a time-dependenthash of the group shared secret, together with an index or identifyingnumber that identifies the selected group shared secret in the store ofL group shared secrets. The authenticating server uses the receivedindex value to locate the corresponding one of the L group sharedsecrets in its memory, and then calculates the hash of this group sharedsecret to determine if it matches the hashed value received from theclient device. If there is a match, then the client device ispre-authenticated.

Because some client devices may share one or more of the same groupshared secrets and the client device is only selecting one of its groupshared secrets to communicate to the authenticating server, it is notuniquely identifying itself in its identification message. However, byincluding in the message the index of the group shared secret that itpurports to possess, it is still communicating the identity of theselected group shared secret. This information could be used by aneavesdropper to track the client device. For example, an eavesdroppercould overhear a particular client device communicating a messagepurporting to identify the group shared secret having index i. The nexttime the eavesdropper overhears a message purporting to identify thegroup shared secret having index i, the eavesdropper may be reasonablyconfident that the message originated at the particular client device.Using the index of the group shared secret selected by the particularclient device, the eavesdropper may track the client device. To avoidthis problem, the index of the group shared secret selected by theclient device may be communicated to the server without disclosing it toeavesdroppers by applying the proposed technique.

In the examples described with respect to FIGS. 6-13, communicationtakes place over a public network (such as the Internet or a similarnetwork), adapted to implement the Internet Protocol Suite (TCP/IP) asdefined in RFC 1122 as published by the Internet Engineering Task Force,and optionally its predecessor, successor, and accompanying orcomplementary standards. Reference to a TCP/IP-based communicationsystem is made due to its prevalence; again, however, the person skilledin the art will appreciate that the examples described herein may beapplied in environments and on networks implementing differentcommunication protocols. For example, other protocols such as the userdatagram protocol (UDP), which may also be provided over IP, can beimplemented as well.

FIG. 6 is a schematic diagram illustrating a first example technique forthe provisioning of group shared secrets by a server 600 to a pluralityof client devices 101, 102 and 103, and the communicating of theidentity of the client device 103's provisioned group shared secret tothe server 600.

The server 600 may store or have access to L group shared secrets 602,including group shared secrets gss₁ 604, gss₂ 606 and gss₃ 608. The Lgroup shared secrets may be identified by L corresponding indices 610,where L may take on any positive integer value. In another example (notshown), each of the L group shared secrets 602 may be identified by anarbitrary identifier. In yet another example (not shown), each of the Lgroup shared secrets 602 may effectively identify itself Typically, thenumber L of group shared secrets 602 will be less than the number ofclient devices that may communicate with the server 600. In one example,the number L of group shared secrets 602 is L=1,000,000. Each one of thegroup shared secrets 602 is a distinct value. In one example, each ofthe group shared secrets 602 is an effectively random value, such thatit cannot be generated again on another occasion, except by chance. Inthis case, the group shared secrets 602 would be stored by the server600 for future reference, for example, in a lookup table. In anotherexample, each of the group shared secrets 602 is a quasi-random orpseudo-random value generated using any suitable generation algorithm,such that the same group shared secret 602 can be reliably generated onanother occasion in a repeatable manner. For example, a particular groupshared secret gss_(i) could be calculated as a hash of a concatenationof a random seed value s and an index i, that is k_(i)=h(s|i), where his any suitable hash algorithm, such as SHA-1, SHA-2, or MD5. In thiscase, the group shared secrets 602 may not be stored by the server 600,provided that the server 600 maintains a record of the conditions underwhich the group shared secrets 602 were generated, including, forexample, the hash algorithm h and the random seed value s. Each one ofthe group shared secrets 602 may be of a sufficient length that itcannot be easily predicted or guessed by an attacker.

The server 600 also stores N group shared secret identifying keys (k₁,k₂, k₃, k₄, k₅, . . . , k_(N)) 612. The N group shared secretidentifying keys may be identified by N corresponding indices (1, 2, 3,4, 5, . . . , N) 614, where N may take on any positive integer value. Inanother example (not shown), each of the N group shared secretidentifying keys 612 may be identified by an arbitrary identifier. Inyet another example (not shown), each of the N group shared secretidentifying keys 612 may effectively identify itself. Typically, thenumber N of group shared secret identifying keys 612 will be less thanthe number of group shared secrets.

Each one of the group shared secret identifying keys 612 is a distinctvalue. In one example, each of the group shared secret identifying keys612 is an effectively random value, such that it cannot be generatedagain on another occasion, except by chance. In this case, the groupshared secret identifying keys 612 would be stored by the server 600 forfuture reference, for example, in a lookup table. In another example,each of the group shared secret identifying keys 612 is a quasi-randomor pseudo-random value generated using any suitable generationalgorithm, such that the same group shared secret identifying key 612can be reliably generated on another occasion in a repeatable manner.For example, a particular group shared secret identifying key k_(i)could be calculated as a hash of a concatenation of a random seed values and an index i, that is k_(i)=h(s|i), where h is any suitable hashalgorithm, such as SHA-1, SHA-2, or MD5. In this case, the group sharedsecret identifying keys 612 may not be stored by the server 600,provided that the server 600 maintains a record of the conditions underwhich the group shared secret identifying keys 612 were generated,including, for example, the hash algorithm h and the random seed values. Each one of the group shared secret identifying keys 612 may be of asufficient length and complexity that it cannot be easily predicted orguessed by an attacker.

In the example illustrated in FIG. 6, the server 600 assigns a subset ofthree of the N group shared secret identifying keys 612 to each one ofthe group shared secrets 602. In particular, the server 600 assigns asubset 616 of group shared secret identifying keys (k₁, k₂, k₃) to thegroup shared secret gss_(l) 604, a subset 618 of group shared secretidentifying keys (k₂, k₃, k₅) to the group shared secret gss₂ 606, and asubset 620 of group shared secret identifying keys (k₂, k₄, k₅) to thegroup shared secret gss₃ 608. The assignment of a subset of the groupshared secret identifying keys 612 to each one of the group sharedsecrets 602 may be carried out in a random, pseudo-random orquasi-random fashion or may be carried out in an arbitrary fashion, andthe server 600 may maintain a record (not shown) of which of the groupshared secret identifying keys 612 were provisioned to which groupshared secret, for example, in the form of a mapping function or alookup table. Alternatively, the assignment of a subset of the groupshared secret identifying keys 612 to each one of the group sharedsecrets 602 may be carried out according to an algorithm. In eithercase, the server 600 may store information (not shown) from which it isdeterminable which of the group shared secret identifying keys 612 wereprovisioned to which group shared secret. Thus, the information maycomprise the relevant mapping function, lookup table, algorithm orinverse thereof, or any other information by which the server 600 candetermine which of the group shared secret identifying keys 612 wereprovisioned to which group shared secret, or can determine to whichgroup shared secret the subset of group shared secret identifying keys612 were assigned.

Some of the group shared secrets 602 may share one or more of the samegroup shared secret identifying keys 612. For example, in FIG. 6, thegroup shared secrets gss₁ 604 and gss₃ 608 have each been assigned thegroup shared secret identifying key k₂. It is also possible that some ofthe group shared secret identifying keys 612 may not yet be assigned toany group shared secret at all, or else that they may be assigned togroup shared secrets that are not illustrated in FIG. 6. In thisexample, it is assumed that no two of the group shared secrets 602 areassigned exactly the same subset of the group shared secret identifyingkeys 612.

In the example illustrated in FIG. 6, the server 600 assigns andprovisions to each of the client devices 101, 102 and 103 a subset oftwo of the group shared secrets 602. In particular, the server 600provisions the group shared secrets gss₁ 604 and gss₂ 606 to the clientdevice 101, the group shared secrets gss₂ 606 and gss₃ 608 to the clientdevice 102, and the group shared secrets gss₁ 604 and gss₃ 608 to theclient device 103. In addition, for each group shared secret provisionedto a client device, the client device also receives the subset of groupshared secret identifying keys assigned to that group shared secret. Forexample, the client device 103 receives the subset 616 of group sharedsecret identifying keys (k₁, k₂, k₃) for the group shared secret gss₁604 and the subset 620 of group shared secret identifying keys (k₂, k₄,k₅) for the group shared secret gss₃ 608.

The subset of the group shared secrets 602 assigned to each clientdevice, and the subset of group shared secret identifying keys 612assigned to each group shared secret, may be embedded in the clientdevice at the time of manufacture, or provisioned at a later date.

The assignment of a subset of the group shared secrets 602 to eachclient device may be carried out in a random, pseudo-random orquasi-random fashion or may be carried out in an arbitrary fashion.Alternatively, the assignment of a subset of the group shared secrets602 to each client device may be carried out according to an algorithm.

As described with respect to FIG. 1 and FIG. 2, the server 600 maypossess a time interval value T that changes from time to time and isagreed on by the server 600 and any provisioned client devices. Forexample, the server 600 might broadcast the current time interval valueT. For each new time interval value T, the server 600 may calculate foreach of the group shared secret identifying keys 612 a hash of acombination of at least the time interval value T and the group sharedsecret identifying key using a hash algorithm H, as describedpreviously. In the example of FIG. 6, the server 600 uses the hashalgorithm H to compute hashes H(T|k₁), H(T|k₂), H(T|k₃), H(T|k₄),H(T|k₅), . . . , H(T|k_(N)), which the server 600 may store in a table622 or some other suitable data structure (not shown). Alternatively,the server 600 may store only portions of the hashes, or some othervalues dependent thereon. In order to account for client devices thatpossess adjacent time interval values T, the server 600 may maintain oneor more additional tables of hash-dependent values (not shown)determined from previous time interval values T or future time intervalvalues T or both. Alternatively, the server 600 may maintain a singletable that includes hash-dependent values determined from the presenttime interval value T and from previous time interval values T or futuretime interval values T or both. Although this description indicates thatthe same hash algorithm H is used to compute the hashes for all groupshared secret identifying keys, different hash algorithms could be usedto compute the hashes for different ones of the group shared secretidentifying keys. That is, a hash algorithm Ha could be used to computethe hash Ha(T|k₁) and a different hash algorithm Hb could be used tocompute the hash Hb(T|k₂), provided that the provisioned client devicealso knows to use the hash algorithm Ha for computing Ha(T|k₁) and thehash algorithm Hb for computing Hb(T|k₂).

For each table of hash-dependent values, the server 600 may associateeach one of the hash-dependent values with the respective one of thegroup shared secret identifying keys 612 from which the hash-dependentvalue was determined (or with the respective index of the group sharedsecret identifying key 612 from which the hash-dependent value wascalculated). The association be implemented as described previously withrespect to FIG. 1. In the example of FIG. 6, the association (not shown)for the table 622 of hash-dependent values would associate each one ofthe hash-dependent values in the table 622 with a corresponding one ofthe group shared secret identifying keys 612 (or with a correspondingone of the indices 614).

The client device 103 may seek to communicate a group shared secret tothe server 600. In the example of FIG. 6, the client device 103 selectsthe group shared secret gss₃ 608 to communicate to the server 600. Thus,for each of the group shared secret identifying keys 620 correspondingto the group shared secret gss₃ 608, the client device 103 may calculatea hash by applying the hash algorithm H to a combination of at least thecurrent time interval value T 624 and the group shared secretidentifying key. The nature of the combination and the definition of thehash algorithm H are the same as that used by the server 600 tocalculate the hashes H(T|k₁), H(T|k₂), H(T|k₃), H(T|k₄), H(T|k₅), . . ., H(T|k_(N)) as described previously. From these hash calculations, theclient device 103 may obtain three hashes 626: H(T|k₂), H(T|k₄), andH(T|k₅). In the same manner that the hashes 214 were used by the server200 to arrive at the identity of the client device 103, the server 600may use the hashes 626 to arrive at the identity of the group sharedsecret gss₃ 608 selected by the client device 103.

In addition to communicating an identity of a group shared secret, theclient device may seek to prove to the server that it possesses thegroup shared secret that it has identified. This may be done bycommunicating an additional hash value to the server. In this example,the client device 103 calculates an additional hash by applying a hashalgorithm G to a combination of at least the current time interval valueT 624 (optionally), the selected group shared secret gss₃ 608, and avalue r 630. From this hash calculation, the client device 103 mayobtain a hash G([T]|gss₃|r) 628, where square brackets are used toindicate that the current time interval value T is optional.Alternatively, a different time interval value could be used in place ofthe time interval value T. The hash algorithm G used to obtain the hash628 may be the same as or different than the hash algorithm H used toobtain the hash 626. In one example, the value r is a pseudo-randomvalue chosen by the client device, and is determined by applying a hashalgorithm to a combination of the current time interval value T and asecret constant C_(CLIENT) specific to the client device.

The client device 103 communicates to the server 600 a messagecomprising the hashes 626, the value r 630, the current time intervalvalue T 624, and the hash 628. The hashes 626 are included so that theclient device 103 can communicate the identity of the group sharedsecret gss₃ 608 that it purports to possess. The hash 628 and the valuer 630 are included so that the client device 103 may prove to the server600 that it possesses the group shared secret gss₃ 608. The value r maybe used to detect replay attacks. For example, if the server 600receives a message comprising a value r that is the same as the value rthat was communicated in a previously received message, the server 600may determine that the current message is a replay attack. In the casethat the value r 630 is related in some way to the time interval value T624, a client device may be prevented from communicating multipleidentification messages is rapid succession. Since the server 600 may beunable to keep a record of every value r ever used, using the timeinterval value T 624 in the calculation of the value r 630 may assurethe server 600 that the value r 630 is not some old value that is beingreplayed. The current time interval value T 624 may also be included inthe message so that the server 600 is privy to which value of the timeinterval value T was used to calculate the hashes 626, and optionallythe hash 628, and so that the server 600 may confirm that client device103 possesses the correct time interval value T.

To determine the identity of the group shared secret that the clientdevice 103 purports to possess, the server 600 proceeds to compare eachone of the hashes 626 to the hashes in the table 622 stored on theserver 600. As described previously with respect to FIG. 1 and FIG. 2,it will be appreciated that, in the case that the server 600 stores onlyportions of hashes or some other values dependent thereon in the table622, the server 600 may use corresponding portions of the hashes 626 orvalues dependent thereon for the comparison. Once the server 600 locatesstored hash-dependent values that are consistent with the receivedhashes 626 or portions thereof or values dependent thereon, the server600 may use the association to determine which of the group sharedsecret identifying keys 612 (or the indices 614) are associated with theconsistent hash-dependent values. In this case, the server 600 may usethe association to determine that the hash-dependent values that areconsistent with the received hashes 626 or portions thereof or valuesdependent thereon are associated with the group shared secretidentifying keys k₂, k₄, k₅ (or with the indices 2, 4 and 5). Now theserver 600 may use the stored information (not shown) from which it isdeterminable which of the group shared secret identifying keys 612 wereassigned to which group shared secret in order to determine which one ofthe group shared secrets 702, if any, was assigned the group sharedsecret identifying keys k₂, k₄, and k₅ (or with the keys having theindices 2, 4 and 5). In this case, the server 600 determines that it wasthe group shared secret gss₃ 608 that was assigned the subset 620 ofgroup shared secret identifying keys (k₂, k₄, k₅).

In this example, no two group shared secrets were assigned exactly thesame subset of the group shared secret identifying keys 612, and thusthe subset 620 of group shared secret identifying keys (k₂, k₄, k₅) isunique to the group shared secret gss₃ 608. It follows that the clientdevice 103 may use the group shared secret identifying keys (k₂, k₄, k₅)to uniquely identify its choice of group shared secret to the server600, and it may do so in a way that cannot be understood or tracked byan eavesdropper from one time interval value T to the next. It will beapparent to those of ordinary skill in the art that, if care is taken inprovisioning, it may be possible for a client device to uniquelyidentify its choice of group shared secret using only some of the groupshared secret identifying keys that were assigned to the group sharedsecret. For example, in this simple case, it will be apparent that thegroup shared secret gss₃ 608 could be uniquely identified to the server200 using only the group shared secret identifying key k₄ because thiskey was not assigned to either of the other group shared secrets gss₁ orgss₂).

At this point, the client device 103 has only communicated to the server600 the identity of the group shared secret that it purports to possess.It has not yet proven that it actually possesses the identified groupshared secret. For example, an eavesdropping device overhearing thehashes 626 could repeat them to the server 600 during the same timeinterval value T 624, and would also be purporting to possess the groupshared secret gss₃ 608. The eavesdropping device may not even be awareof which group shared secret it is purporting to possess.

In order to verify that the client device 103 actually possesses thegroup shared secret gss₃ 608 that it has identified, the server 600 maycalculate an additional hash (not shown) by applying the hash algorithmG to a combination of at least the current time interval value T(optionally), the group shared secret gss₃ 608, and the value r 630 thatit received from the client device 103. From this hash calculation, theserver 600 may obtain a calculated hash G([T]|gss₃|r) (not shown). Thenature of the combination and definition of the hash algorithm G are thesame as that used by the client device 103 to obtain the hash 628. Theserver 600 may then compare the calculated hash (not shown) to the hash628 received from the client device 103. Alternatively, the server 600may only compare corresponding portions of the calculated hash and thehash 628, or values dependent thereon. If the hash-dependent values areconsistent, the server 600 may determine that the client device 103possesses the group shared secret key gss₃ 608 that it has identified.

While the server 600 is illustrated as a single device, it iscontemplated that the server 600 may comprise multiple devices. Forexample, the server 600 may comprise one or more provisioning servers,each of which is configured to provision one or more of the group sharedsecrets 702 and the group shared secret identifying keys 612 to one ormore client devices. The server 600 may also comprise one or morereceiving servers, each of which is able to receive a message purportingto identify a group shared secret and prove the sender's possession ofthe identified group shared secret. The calculation of the hashesH(T|k₁), H(T|k₂), H(T|k₃), H(T|k₄), H(T|k₅), . . . , H(T|k_(N)) and thedetermination of the hash-dependent values to be stored in the table 622for a particular time interval value T may be performed by the one ormore provisioning servers or by the one or more receiving servers or bysome combination thereof. For example, the one or more provisioningservers may share information with the one or more receiving servers,such as any of the group shared secrets 702, any of the group sharedsecret identifying keys 612 and the information from which it isdeterminable which group shared secret identifying keys were assigned towhich group shared secret. In one example, the shared information isstored on one or more databases accessible by the one or moreprovisioning servers and the one or more receiving servers. In anotherexample, in the case of more than one receiving server, each receivingserver may only be able to identify a subset of the group sharedsecrets. For example, the receiving server may not have access to all ofthe group shared secret identifying keys or to the information fromwhich it is determinable which group shared secret identifying keys wereprovisioned to which group shared secret.

FIG. 7 is a flowchart illustrating a first example method to beperformed by a provisioning server for provisioning group shared secretsto client devices.

The method begins at 700 by having the provisioning server store or haveaccess to a plurality of L group shared secrets (gss₁, gss₂, . . . ,gss_(L)), also denoted as group shared secrets {gss_(q)}. The L groupshared secrets may be identified by indices (1, 2, . . . , L), where Lmay take on any positive integer value. Alternatively, each of the groupshared secrets {gss_(q)} may be identified by an arbitrary identifier ormay effectively identify itself. The provisioning server also stores orhas access to a plurality of N group shared secret identifying keys (k₁,k₂, . . . , k_(N)). The N group shared secret identifying keys may beidentified by indices (1, 2, . . . , N). Alternatively, each of thegroup shared secret identifying keys (k₁, k₂, . . . , k_(N)) may beidentified by an arbitrary identifier or may effectively identifyitself.

Each one of the group shared secrets {gss_(q)} and the group sharedsecret identifying keys (k₁, k₂, . . . , k_(N)) is a distinct value,such as an effectively random value, a quasi-random or a pseudo-randomvalue, or a value that can be reliably generated on another occasion ina repeatable manner. In the latter case, it will be appreciated that theserver may not explicitly store the group shared secrets {gss_(q)}and/or the group shared secret identifying keys (k₁, k₂, . . . , k_(N)),provided that the server maintains a record of the conditions underwhich the group shared secrets and/or the group shared secretidentifying keys were generated. Each one of the group shared secrets{gss_(q)} and the group shared secret identifying keys (k₁, k₂, . . . ,k_(N)) may be of a sufficient length and complexity that it cannot beeasily predicted or guessed by an attacker

At 702, the provisioning server assigns to each group shared secretgss_(q) a unique subset of M_(q) group shared secret identifying keys(k_(G1), k_(G2), . . . , k_(GMq)) selected from the N group sharedsecret identifying keys (k₁, k₂, . . . , k_(N)), where M_(q) is apositive integer less than N. In the example illustrated in FIG. 6, thenumber M_(q) of group shared secret identifying keys in the subset forall group shared secrets {gss_(q)} is M_(q)=3. In other examples, someof the group shared secrets {gss_(q)} may have more group shared secretidentifying keys provisioned thereto than others of the group sharedsecrets {gss_(q)}. In the present example, all group shared secrets{gss_(q)} are provisioned with a subset of M_(q)=M group shared secretidentifying keys. The assignment of the subsets of group shared secretidentifying keys to the group shared secrets {gss_(q)} may be carriedout in a random, pseudo-random or quasi-random fashion or may be carriedout in an arbitrary fashion, and the server may maintain a record ofwhich of the N group shared secret identifying keys (k₁, k₂, . . . ,k_(N)) were assigned to which group shared secret gss_(q), for example,in the form of a mapping function or a lookup table. Alternatively, theassignment of the subsets of group shared secret identifying keys to thegroup shared secrets {gss_(q)} may be carried out according to analgorithm. As noted previously, two or more group shared secrets may beassigned one or more of the same group shared secret identifying keys,provided that no two group shared secrets are assigned the exact samesubset (km, k_(G2), . . . , k_(GM)) of the group shared secretidentifying keys (k₁, k₂, . . . , k_(N)). It is also possible that someof the group shared secret identifying keys (k₁, k₂, . . . , k_(N)) maynot be assigned to any group shared secret at all.

At 704, the provisioning server may store information from which it isdeterminable which M group shared secret identifying keys were assignedto which group shared secret. The information may comprise the relevantmapping function, lookup table, algorithm or inverse thereof, or anyother information by which the server can determine which of the groupshared secret identifying keys were assigned to which group sharedsecret.

At 706, the provisioning server assigns to each client device j to beprovisioned a subset of P_(j) group shared secrets (gss_(C1), gss_(C2),. . . , gss_(CPj)) selected from the L group shared secrets (gss_(j),gss₂, . . . , gss_(L)), where P_(j) is a positive integer less than L.In the example illustrated in FIG. 6, the number P_(j) of group sharedsecrets in the subset for all client devices {j} is P_(j)=2. In otherexamples, some of the client devices {j} may have more group sharedsecrets provisioned thereto than others of the client devices {j}. Inthe present example, all client devices {j} are provisioned with asubset of P_(j)=P group shared secret identifying keys. The assignmentof the subsets of group shared secrets to the client devices {j} may becarried out in a random, pseudo-random or quasi-random fashion or may becarried out in an arbitrary fashion. Alternatively, the assignment ofthe subsets of group shared secrets to the client devices {j} may becarried out according to an algorithm. Two or more client devices may beassigned one or more of the same group shared secrets. It is alsopossible that some of the group shared secrets {gss_(q)} may not yet beassigned to any client device at all.

It should be noted that if two client devices are provisioned with anidentical subset of P of the L group shared secrets, and all of those Pgroup shared secrets are compromised, both of the client devices will becompromised as a result. To avoid this, each client device may beprovisioned with a unique subset of P group shared secrets. Thus, if aclient device happens to select from its subset a group shared secretthat is compromised, it may still proceed to attempt to identify anotherone of its P group shared secrets.

At 708, the provisioning server provides to each client device to beprovisioned its respective assigned subset of P group shared secrets(gss_(C1), gss_(C2), . . . , gss_(CP)). In addition, for each one of theP group shared secrets (gss_(C1), gss_(C2), . . . , gss_(CP)), theprovisioning server provides to the client device the unique subset of Mgroup shared secret identifying keys (k_(G1), k_(G2), . . . , k_(GM))assigned to that group shared secret. The subset of P group sharedsecrets (gss_(C1), gss_(C2), . . . , gss_(CP)) assigned to each clientdevice, and the unique subset of M group shared secret identifying keys(k_(G1), k_(G2), . . . , k_(GM)) assigned to each group shared secret,may be embedded in a client device at the time of manufacture, orprovisioned at a later date, for example, via a storage module such as aSIM, or via a transmission over a secure channel.

FIG. 8 is a flowchart illustrating a first example method to beperformed by a provisioned client device for communicating one of itsprovisioned group shared secrets to a receiving server.

At 800, the client device receives from a provisioning server a subsetof P group shared secrets (gss_(C1), gss_(C2), . . . , gss_(CP)) and,for each one of the P group shared secrets, the client device receives aunique subset of M group shared secret identifying keys (k_(G1), k_(G2),. . . , k_(GM)). As described above, the subset of P group sharedsecrets (gss_(C1), gss_(C2), . . . , gss_(CP)), and the unique subset ofM group shared secret identifying keys (k_(G1), k_(G2), . . . , k_(GM))assigned to each group shared secret, may be embedded in the clientdevice at the time of manufacture, or received at a later date.

At some point after being provisioned with its subset of group sharedsecrets (gss_(C1), gss_(C2), . . . , gss_(CP)) and the unique subsets ofgroup shared secret identifying keys (k_(G1), k_(G2), . . . , k_(GM))corresponding to each group shared secret, the client device maydetermine at 802 that it has a need to communicate a group shared secretto a server. For example, it may seek to pre-authenticate itself to aweb server.

Once the client device determines at 802 that it has a need tocommunicate a group shared secret to the server, the client device mayproceed at 804 to select one of its P group shared secrets (gss_(C1),gss_(C2), . . . , gss_(CP)) to communicate to the server. The selectedgroup shared secret is denoted gss_(C1).

At 806, the client device may proceed to calculate, for each of the Mgroup shared secret identifying keys assigned to the selected groupshared secret gss_(Ci), a hash by applying a hash algorithm H to acombination of at least the current time interval value T and the groupshared secret identifying key, thereby obtaining M hashes: H(T|k_(G1)),H(T|k_(G2)), H(T|k_(GM)). Although not explicitly shown, the clientdevice may receive one or more of the current time interval value T, anindication of the hash algorithm H, and an indication of the nature ofthe combination via a broadcast from the provisioning server or areceiving server.

At 808, the client device calculates another hash by application a hashalgorithm G to a combination of the current time interval value T(optionally), the selected group shared secret gss_(Ci), and a value r,thereby obtaining a hash G([T]|gss_(Ci)|r), where the value r is used todetect replay attacks as described previously.

At 810, the client device communicates a message to the servercomprising each one of the M hashes H(T|k_(G1)), H(T|k_(G2)), . . . ,H(T|k_(GM)) calculated at 806, the value r, the current time intervalvalue T, and the hash G([T]|gss_(Ci)|r) calculated at 808. Alternativelyto including each of the M hashes H(T|k_(G1)), H(T|k_(G2)), . . . ,H(T|k_(GM)) in its entirety in the message, the client device mayinclude only portions of the M hashes or values dependent thereon.Similarly, the client device may include a portion of the hashG([T]|gss_(Ci)|r) or a value dependent thereon. The order of the valuesin the message may be agreed on by the server and the provisioned clientdevices.

The methods described herein are based on the assumption that each groupshared secret is assigned the same number M of group shared secretidentifying keys. However, it will be apparent to a person of ordinaryskill in the art that different group shared secrets may be assigneddifferent numbers of group shared secret identifying keys, provided thatno group shared secret is assigned a subset of another group sharedsecret's group shared secret identifying keys. In one example, a clientdevice may indicate in the message communicated at 810 the number ofgroup shared secret identifying keys to which the message pertains.

FIGS. 9-1 and 9-2 are flowcharts illustrating a first example method tobe performed by a receiving server for determining whether a receivedmessage from a client device identifies a group shared secret andwhether the client device possesses the identified group shared secret.The receiving server may be the same server as the provisioning serverthat is configured to perform the method illustrated in FIG. 7.Alternatively, the receiving server may be a separate server from theprovisioning server, but may share information with the provisioningserver, including, for example, the group shared secrets (gss₁, gss₂, .. . , gss_(L)), the group shared secret identifying keys (k₁, k₂, . . ., k_(N)) and the information from which it is determinable which M_(q)group shared secret identifying keys were assigned to which group sharedsecret gss_(q). In one example, the shared information is stored on oneor more databases accessible by the provisioning server and thereceiving server.

The method illustrated in FIG. 9-1 begins at 900 by having the serverstore or have access to the L of group shared secrets (gss₁, gss₂, . . ., gss_(L)), as well as the N group shared secret identifying keys (k₁,k₂, . . . , k_(N)). The server also stores or has access to theinformation from which it is determinable which M_(q) group sharedsecret identifying keys (k_(G1), k_(G2), . . . , k_(GM)) were assignedto which group shared secret gss_(q). In this example, all group sharedsecrets {gss_(q)} have been assigned a subset M_(q)=M group sharedsecret identifying keys.

At 902, the server calculates for each of the N group shared secretidentifying keys a hash of a combination of at least the current timeinterval value T and the group shared secret identifying key, therebyobtaining N hashes: H(T|k₁), H(T|k₂), . . . , H(T|k_(N)). The nature ofthe combination and the hash algorithm H are the same as that used bythe client device to calculate hashes at 808.

In another example, not shown in FIGS. 8 and 9-1, the client device andthe server may include the index of the group shared secret identifyingkey in each of the hash calculations performed at 806 and 902,respectively. Thus, instead of calculating M hashes H(T|k_(G1)),H(T|k_(G2)), . . . , H(T|k_(GM)), the client device may calculate Mhashes H(T|G1|k_(G1)), H(T|G2|k_(G2)), . . . , H(T|GM|k_(GM)).Similarly, instead of calculating N hashes H(T|k₁), H(T|k₂), . . . ,H(T|k_(N)), the server may calculate N hashes H(T|1|k₁), H(T|2|k₂), . .. , H(T|N|k_(N)).

At 904, the server may store each of the N calculated hashes or portionsthereof or values dependent thereon as hash-dependent values in a tableor some other suitable data structure. Although not shown, the servermay store one or more additional tables of hash-dependent valuesdetermined from previous time interval values T or future time intervalvalues T or both. Alternatively, the server may maintain a single tablethat includes hash-dependent values determined from the present timeinterval value T and from previous time interval values T or future timeinterval values T or both.

At 906, for each table of hash-dependent values, the server associateseach one of the N hash-dependent values in the table with the respectiveone of the N group shared secret identifying keys from which thehash-dependent value was determined (or with the respective index of theone of the N group shared secret identifying keys (k₁, k₂, . . . ,k_(N)) from which the hash-dependent value was determined).

At 908, the server checks whether it has received a message purportingto identify a group shared secret. If the server does not receive anysuch message, and if the server determines at 910 that the time intervalvalue T has increased, the server proceeds to repeat the calculation ofthe N hashes H(T|k₁), H(T|k₂), . . . , H(T|k_(N)) at 902 using the newtime interval value T. The server may then store new hash-dependentvalues at 904, and generate at 906 the association of each one of thenew hash-dependent values with the respective one of the N group sharedsecret identifying keys from which the new hash-dependent value wasdetermined (or with the respective index of the one of the N groupshared secret identifying keys from which the hash-dependent value wasdetermined). As noted above, since the server may store additionalhash-dependent values determined from previous time interval values T orfuture time interval values T or both, the new hash-dependent values mayor may not overwrite previously stored hash-dependent values. Severaltables of hash-dependent values and associations may be maintained atany one time.

Once the server determines at 908 that it has received a messagepurporting to identify a group shared secret, the server may proceed todetermine at 912 whether the message identifies a group shared secretand whether the client device from which the message was receivedpossesses the identified group shared secret.

The determination made at 912 is described in more detail by the actionsillustrated in FIG. 9-2.

At 914, the server extracts from the received message values purportingto be: the hashes H(T|k_(G1)), H(T|k_(G2)), . . . , H(T|k_(GM)) orportions thereof or values dependent thereon, as well as the value r,the current time interval value T, and the hash G([T]|gss_(Ci)|r) or aportion thereof or value dependent thereon. Extraction of the componentsmay occur separately for each individual component. Alternatively, inthe case that the components have been combined, for example, using aBloom filter, extraction of the components may be understood asreferring to the extraction of the combination.

At 916, the server compares each one of the M extracted hashesH(T|k_(G1)), H(T|k_(G2)), . . . , H(T|k_(GM)) or relevant portionsthereof or values dependent thereon to each value in the table ofhash-dependent values stored at 904, or optionally to hash-dependentvalues stored in one or more additional tables. This may be done untilthe server locates hash-dependent values that are consistent with eachof the M extracted values in the received message.

At 918, the server checks whether there are stored hash-dependent valuesthat are consistent with each of the M extracted hashes H(T|k_(G1)),H(T|k_(G2)), . . . , H(T|k_(GM)) or relevant portions thereof or valuesdependent thereon. If the server determines at 918 that one or more ofthe M extracted hashes or relevant portions thereof or values dependentthereon are not consistent with any stored hash-dependent value, theserver can determine with certainty at 920 that the client device is notidentifying a group shared secret.

If the server determines at 918 that each of the M extracted hashesH(T|k_(G1)), H(T|k_(G2)), . . . , H(T|k_(GM)) or portions thereof orvalues dependent thereon is consistent with a stored hash-dependentvalue, the server may proceed to use the association at 922 to determinethe group shared secret identifying key (or the index of the groupshared secret identifying key) that is associated with each consistenthash-dependent value. At 924, the server may use the information storedat 900 (i.e., the information from which it is determinable which Mgroup shared secret identifying keys were assigned to which group sharedsecret) to determine which group shared secret gss_(Ci), if any, wasassigned the group shared secret identifying keys determined at 922.Although not explicitly shown, if the server determines at 924 thatthere is no group shared secret that was assigned the group sharedsecret identifying keys determined at 922, the server may determine thatthe client device is not identifying a group shared secret and themethod may end.

In order to verify that the client device from which the message isreceived actually possesses the identified group shared secret gss_(Ci),the server may calculate at 926 an additional hash by applying the hashalgorithm G to a combination of at least the current time interval valueT (optionally), the identified group shared secret gss_(Ci) identifiedat 924, and the value r that it extracted from the received message at914. From this hash calculation, the server may obtain a calculated hashG([T]|gss_(Ci)|r). The nature of the combination and definition of thehash algorithm G are the same as that used by the client device toobtain the hash at 808. At 928, the server may compare the calculatedhash to the hash G([T]|gss_(Ci)|r) that it extracted from the receivedmessage at 914. Alternatively, the server may only compare correspondingportions of the calculated hash and the received hash, or valuesdependent thereon. The server checks at 930 whether the hashes areconsistent. If the hashes are consistent, the server may determine at934 that the client device possesses the group shared secret gss_(Ci)that it has identified. If the server determines at 930 that the hashesare not consistent, the server may determine at 932 that the clientdevice does not possess the group shared secret gss_(Ci) that it hasidentified.

The proposed technique permits a client device to communicate its choiceof group shared secret in a way that cannot be understood byeavesdroppers. While an eavesdropping device may overhear the hashesH(T|k_(G1)), H(T|k_(G2)), . . . , H(T|k_(GM)) or portions thereof orvalues dependent thereon communicated by a particular client device, theeavesdropping device cannot determine the group shared secretidentifying keys from which the hash-dependent values were obtained, andtherefore cannot infer the identity of the group shared secret.Furthermore, since the hash-dependent values communicated by each clientdevice change with each new time interval value T, it is not possiblefor a client device to be tracked by the eavesdropping device from onetime interval value T to the next.

Rather than identifying each group shared secret by a plurality of groupshared secret identifying keys, it may be possible to simplify thetechnique by identifying each group shared secret by a single groupshared secret identifying key. The technique may be further simplifiedif each group shared secret identifying key and the group shared secretthat it identifies are in fact one and the same. This may be betterunderstood with reference to FIGS. 10-13.

FIG. 10 is a schematic diagram illustrating a second example techniquefor the provisioning of group shared secrets by a server 1000 to aplurality of client devices 101, 102 and 103, and the communicating ofthe identity of the client device 103's provisioned group shared secretto the server 1000.

Similarly to the server 600 illustrated in FIG. 6, the server 1000 maystore or have access to L group shared secrets 702, including groupshared secrets gss₁ 604, gss₂ 606 and gss₃ 608, and L correspondingindices 610. Using this simplified technique, the server 1000 does notneed to store a separate set of group shared secret identifying keyssince the group shared secrets effectively identify themselves.

In the example illustrated in FIG. 10, the server 1000 assigns andprovisions to each of the client devices 101, 102 and 103 a subset oftwo of the group shared secrets 702. In particular, as described withrespect to FIG. 6, the server 600 provisions group shared secrets gss₁604 and gss₂ 606 to the client device 101, a group shared secrets gss₂606 and gss₃ 608 to the client device 102, and group shared secrets gss₁604 and gss₃ 608 to the client device 103.

As described with respect to FIG. 6, for each new time interval value T,the server 1000 may calculate for each of the group shared secrets 702 ahash of a combination of at least the current time interval value T andthe group shared secret. In the example of FIG. 10, the server 1000 usesthe hash algorithm H to compute hashes: H(T|gss₁), H(T|gss₂), H(T|gss₃),. . . , H(T|gss_(L)), which the server 1000 may store in a table 1022 orsome other suitable data structure (not shown). Alternatively, theserver 1000 may store only portions of the hashes, or some other valuesdependent thereon. The server 1000 may maintain one or more additionaltables of hash-dependent values (not shown) determined from previoustime interval values T or future time interval values T or both.Alternatively, the server 1000 may maintain a single table that includeshash-dependent values determined from the present time interval value Tand from previous time interval values T or future time interval valuesT or both. For each table of hash-dependent values, the server 1000 mayassociate each one of the hash-dependent values with the respective oneof the group shared secrets 702 from which the hash-dependent value wasdetermine (or with the respective one of the indices 610).

The client device 103 may seek to communicate a group shared secret tothe server 1000. In the example of FIG. 10, the client device 103selects the group shared secret gss₃ 608 to communicate to the server1000. Thus, the client device 103 may calculate a hash by applying thehash algorithm H to a combination of at least the current time intervalvalue T 624 and the group shared secret gss₃ 608. The nature of thecombination and the definition of the hash algorithm H are the same asthat used by the server 1000 to calculate the hashes H(T|gss₁),H(T|gss₂), H(T|gss₃), . . . , H(T|gss_(L)) as described previously. Fromthis hash calculation, the client device 103 may obtain a hash H(T|gss₃)1002. In contrast to the technique illustrated in FIG. 6, instead ofusing the hashes H(T|k₂), H(T|k₄), and H(T|k₅) 626 to communicate theidentity of the group shared secret gss₃ 608 to the server, the clientdevice 103 may use the single hash value H(T|gss₃) 1002 to communicatethe identity of the group shared secret gss₃ 608.

As described with respect to FIG. 6, the client device may also seek toprove to the server that it possesses the group shared secret that ithas identified. As before, this may be done by having the client device103 calculate the additional hash G([T]|gss₃|r) 628.

The client device 103 communicates to the server 1000 a messagecomprising the hash 1002, the value r 630, the current time intervalvalue T 624, and the hash 628. The hash 1002 is included so that theclient device 103 can communicate the identity of the group sharedsecret gss₃ 608 that it purports to possess. The hash 628 and the valuer 630 are included so that the client device 103 may prove to the server1000 that it possesses the group shared secret gss₃ 608. The currenttime interval value T 624 may be included so that the server 1000 isprivy to which value of the time interval value T was used to calculatethe hash 1002, and optionally the hash 628, and so that the server 1000may confirm that client device 103 possesses the correct time intervalvalue T.

To determine the identity of the group shared secret that the clientdevice 103 purports to possess, the server 1000 proceeds to compare thehash 1002 to the hashes in the table 1022 stored on the server 1000. Inthe case that the server 1000 stores only portions of hashes or someother values dependent thereon in the table 1022, the server 1000 mayuse a corresponding portion of the hash 1002 or a value dependentthereon for the comparison. Once the server 1000 locates a storedhash-dependent value that is consistent with the received hash 1002 or aportion thereof or value dependent thereon, the server 1000 may use theassociation to determine which of the group shared secrets 702 (or theindices 610) is associated with the consistent hash-dependent value. Inthis case, the server 1000 may use the association to determine that thehash-dependent value that is consistent with the received hash 1002 orportion thereof or value dependent thereon is associated with the groupshared secret gss₃ 608 (or with the index 3). By following the exampletechnique illustrated in FIG. 10, the client device 103 is effectivelycommunicating an identity of its choice of group shared secret to theserver 1000, and is doing so in a way that cannot be understood ortracked by an eavesdropper from one time interval value T to the next.

At this point, the client device 103 has only communicated to the server1000 the identity of the group shared secret that it purports topossess. It has not yet proven that it actually possesses the identifiedgroup shared secret. For example, an eavesdropping device overhearingthe hash 1002 could repeat it to the server 1000 during the same timeinterval value T 624, and would also be purporting to possess the groupshared secret gss₃ 608. The eavesdropping device may not even be privyto which group shared secret is purporting to possess.

In order to verify that the client device 103 actually possesses thegroup shared secret gss₃ 608 that it has identified, the server 1000 maycalculate an additional hash (not shown) by applying the hash algorithmG to a combination of at least the current time interval value T(optionally), the group shared secret gss₃ 608, and the value r 630 thatit received from the client device 103. From this hash calculation, theserver 1000 may obtain a calculated hash G([T]|gss₃|r) (not shown). Theserver 1000 may then compare the calculated hash (not shown) to the hash628 received from the client device 103. Alternatively, the server 1000may only compare corresponding portions of the calculated hash and thehash 628, or values dependent thereon. If the hash-dependent values areconsistent, the server 1000 may determine that the client device 103possesses the group shared secret key gss₃ 608 that it has identified.

While the server 1000 is illustrated as a single device, it iscontemplated that the server 1000 may comprise multiple devices. Forexample, the server 1000 may comprise one or more provisioning servers,each of which is configured to provision one or more of the group sharedsecrets 702 to one or more client devices. The server 1000 may alsocomprise one or more receiving servers, each of which is able to receivea message purporting to identify a group shared secret and prove thesender's possession of the identified group shared secret. Thecalculation of the hashes 1022 and the determination of thehash-dependent values to be stored for a particular time interval valueT may be performed by the one or more provisioning servers or by the oneor more receiving servers or by some combination thereof. For example,the one or more provisioning servers may share information with the oneor more receiving servers, such as any of the group shared secrets 702.In one example, the shared information is stored on one or moredatabases accessible by the one or more provisioning servers and the oneor more receiving servers. In another example, in the case of more thanone receiving server, each receiving server may only be able to identifya subset of the group shared secrets. For example, the receiving servermay not have access to all of the group shared secret identifying keysor to the information from which it is determinable which group sharedsecret identifying keys were provisioned to which group shared secret.

FIG. 11 is a flowchart illustrating a second example method to beperformed by a provisioning server for provisioning group shared secretsto client devices.

The method begins at 1100 by having the provisioning server store orhave access to a plurality of L group shared secrets (gss₁, gss₂, . . ., gss_(L)), also denoted as group shared secrets {gss_(q)}. The L groupshared secrets may be identified by indices (1, 2, . . . , L), where Lmay take on any positive integer value. Alternatively, each of the groupshared secrets {gss_(q)} may be identified by an arbitrary identifier ormay effectively identify itself. Each one of the group shared secrets{gss_(q)} is a distinct value, such as an effectively random value, aquasi-random or a pseudo-random value, or a value that can be reliablygenerated on another occasion in a repeatable manner. In the lattercase, it will be appreciated that the server may not explicitly storethe group shared secrets {gss_(q)}, provided that the server maintains arecord of the conditions under which the group shared secrets weregenerated. Each one of the group shared secrets {gss_(q)} may be of asufficient length and complexity that it cannot be easily predicted orguessed by an attacker

At 1102, the provisioning server assigns to each client device j to beprovisioned a subset of P_(j) group shared secrets (gss_(C1), gss_(C2),. . . , gss_(CPj)) selected from the L group shared secrets (gss₁, gss₂,. . . , gss_(L)), where P_(j) is a positive integer less than L. In theexample illustrated in FIG. 10, the number P_(j) of group shared secretsin the subset for all client devices {j} is P_(j)=2. In other examples,some of the client devices {j} may have more group shared secretsprovisioned thereto than others of the client devices {j}. In thepresent example, all client devices {j} are provisioned with a subset ofP_(j)=P group shared secret identifying keys. The assignment of thesubsets of group shared secrets to the client devices {j} may be carriedout in a random, pseudo-random or quasi-random fashion or may be carriedout in an arbitrary fashion. Alternatively, the assignment of thesubsets of group shared secrets to the client devices {j} may be carriedout according to an algorithm. Two or more client devices may beassigned one or more of the same group shared secrets. It is alsopossible that some of the group shared secrets {gss_(q)} may not yet beassigned to any client device at all.

At 1104, the provisioning server provides to each client device to beprovisioned its respective assigned subset of P group shared secrets(gss_(C1), gss_(C2), . . . , gss_(CP)). The subset of P group sharedsecrets (gss_(C1), gss_(C2), . . . , gss_(CP)) assigned to each clientdevice may be embedded in a client device at the time of manufacture, orprovisioned at a later date, for example, via a storage module such as aSIM, or via a transmission over a secure channel.

FIG. 12 is a flowchart illustrating a second example method to beperformed by a provisioned client device for communicating one of itsprovisioned group shared secrets to a receiving server.

At 1200, the client device receives from a provisioning server a subsetof P group shared secrets (gss_(C1), gss_(C2), . . . , gss_(CP)). The Pgroup shared secrets (gss_(C1), gss_(C2), . . . , gss_(CP)) may beembedded in the client device at the time of manufacture, or received ata later date.

At some point after being provisioned with its subset of group sharedsecrets (gss_(C1), gss_(C2), . . . , gss_(CP)), the client device maydetermine at 1202 that it has a need to communicate a group sharedsecret to a server.

Once the client device determines at 1202 that it has a need tocommunicate a group shared secret to the server, the client device mayproceed at 1204 to select one of its P group shared secrets (gss_(C1),gss_(C2), . . . , gss_(CP)) to communicate to the server. The selectedgroup shared secret is denoted gss_(Ci).

At 1206, the client device may proceed to calculate a hash by applying ahash algorithm H to a combination of at least the current time intervalvalue T and the selected group shared secret gss_(Ci), thereby obtaininga hash H(T|gss_(Ci)). Although not explicitly shown, the client devicemay receive one or more of the current time interval value T, anindication of the hash algorithm H, and an indication of the nature ofthe combination via a broadcast from the provisioning server or areceiving server.

At 1208, the client device calculates another hash by application a hashalgorithm G to a combination of the current time interval value T(optionally), the selected group shared secret gss_(Ci), and a value r,thereby obtaining a hash G([T]|gss_(Ci)|r), where the value r is used todetect replay attacks as described previously.

At 1210, the client device communicates a message to the servercomprising the hash H(T|gss_(C1)) calculated at 1206, the value r, thecurrent time interval value T, and the hash G([T]|gss_(Ci)|r) calculatedat 1208. Alternatively to including the hash H(T|gss_(C1)) in itsentirety in the message, the client device may include only a portion ofthe hash H(T|gss_(C1)) or a value dependent thereon. Similarly, theclient device may include a portion of the hash G([T]|gss_(Ci)|r) or avalue dependent thereon. The order of the values in the message may beagreed on by the server and the provisioned client devices.

FIGS. 13-1 and 13-2 are flowcharts illustrating a second example methodto be performed by a receiving server for determining whether a receivedmessage from a client device identifies a group shared secret andwhether the client device possesses the identified group shared secret.

The receiving server may be the same server as the provisioning serverthat is configured to perform the method illustrated in FIG. 11.Alternatively, the receiving server may be a separate server from theprovisioning server, but may share information with the provisioningserver, including, for example, the group shared secrets (gss₁, gss₂, .. . , gss_(L)). In one example, the shared information is stored on oneor more databases accessible by both the provisioning server and thereceiving server.

The method illustrated in FIG. 13-1 begins at 1300 by having the serverstore or have access to the L of group shared secrets (gss₁, gss₂, . . ., gss_(L)).

At 1302, the server calculates for each of the L group shared secrets ahash of a combination of at least the current time interval value T andthe group shared secret, thereby obtaining L hashes: H(T|gss₁),H(T|gss₂), . . . , H(T|gss_(L)). The nature of the combination and thehash algorithm H are the same as that used by the client device tocalculate hash at 1206.

In another example, not shown in FIGS. 12 and 13-1, the client deviceand the server may include the index of the group shared secret in thehash calculations performed at 1206 and 1302, respectively. Thus,instead of calculating the hash H(T|gss_(C1)), the client device maycalculate the hash H(T|Ci|gss_(Ci)). Similarly, instead of calculating Lhashes H(T|gss₁), H(T|gss₂), . . . , H(T|gss_(L)), the server maycalculate L hashes H(T|1|gss_(i)), H(T|2|gss₂), . . . , H(T|L|gss_(L)).As noted previously, including an index as salt in a hash calculationmay make the hash value harder to attack.

At 1304, the server may store each of the L calculated hashes orportions thereof or values dependent thereon as hash-dependent values ina table or some other suitable data structure. Although not shown, theserver may store one or more additional tables of hash-dependent valuesdetermined from previous time interval values T or future time intervalvalues T or both. Alternatively, the server may maintain a single tablethat includes hash-dependent values determined from the present timeinterval value T and from previous time interval values T or future timeinterval values T or both.

At 1306, for each table of hash-dependent values, the server associateseach one of the L hash-dependent values with the respective one of the Lgroup shared secrets from which the hash-dependent value was determined(or with the respective index of the one of the L group shared secrets(gss₁, gss₂, . . . , gss_(L)) from which the hash-dependent value wasdetermined).

At 1308, the server checks whether it has received a message purportingto identify a group shared secret. If the server does not receive anysuch message, and if the server determines at 1310 that the timeinterval value T has increased, the server proceeds to repeat thecalculation of the L hashes H(T|gss₁), H(T|gss₂), . . . , H(T|gss_(L))at 1302 using the new time interval value T. The server may then storenew hash-dependent values at 1304, and generate at 1306 the associationthat associates each one of the new hash-dependent values with therespective one of the L group shared secrets from which the newhash-dependent value was determined (or with the respective index of theone of the L group shared secrets from which the hash-dependent valuewas determined). As noted above, since the server may store additionalhash-dependent values determined from previous time interval values T orfuture time interval values T or both, the new hash-dependent values mayor may not overwrite previously stored hash-dependent values. Severaltables of hash-dependent values and associations may be maintained atany one time.

Once the server determines at 1308 that it has received a messagepurporting to identify a group shared secret, the server may proceed todetermine at 1312 whether the message identifies a group shared secretand whether the client device from which the message was receivedpossesses the identified group shared secret.

The determination made at 1312 is described in more detail by theactions illustrated in FIG. 13-2.

At 1314, the server extracts from the received message values purportingto be: the hash H(T|gss_(Ci)) or a portion thereof or value dependentthereon, as well as the value r, the current time interval value T, andthe hash G([T]|gss_(Ci)|r) or a portion thereof or value dependentthereon. Extraction of the components may occur separately for eachindividual component. Alternatively, in the case that the componentshave been combined, for example, using a Bloom filter, extraction of thecomponents may be understood as referring to the extraction of thecombination.

At 1316, the server compares the extracted hash H(T|gss_(C1)) orrelevant portion thereof or value dependent thereon, to each value inthe table of hash-dependent values stored at 1304, or optionally tohash-dependent values stored in one or more additional tables. This maybe done until the server locates a hash-dependent value that isconsistent with the extracted value in the received message.

At 1318, the server checks whether there is any stored hash-dependentvalue that is consistent with the extracted value H(T|gss_(Ci)) orrelevant portion thereof or value dependent thereon. If the serverdetermines at 1318 that the extracted hash H(T|gss_(Ci)) or relevantportion thereof or value dependent thereon is not consistent with anystored hash-dependent value, the server can determine with certainty at1320 that the client device is not identifying a group shared secret.

If the server determines at 1318 that the extracted hash H(T|gss_(Ci))or a portion thereof or value dependent thereon is consistent with astored hash-dependent value, the server may proceed to use theassociation at 1322 to determine the group shared secret gss_(Ci) (orthe index Ci of the group shared secret gss_(Ci)) that is associatedwith the consistent hash-dependent value.

In order to verify that the client device from which the message isreceived actually possesses the identified group shared secret gss_(Ci),the server may calculate at 1324 an additional hash by applying the hashalgorithm G to a combination of at least the current time interval valueT (optionally), the group shared secret gss_(Ci) identified at 1322, andthe value r that it extracted from the received message at 1314. Fromthis hash calculation, the server may obtain a calculated hash valueG([T]|gss_(Ci)|r). The nature of the combination and definition of thehash algorithm G are the same as that used by the client device toobtain the hash 1208. At 1326, the server may compare the calculatedhash to the hash G([T]|gss_(Ci)|r) that it extracted from the receivedmessage at 1314. Alternatively, the server may only comparecorresponding portions of the calculated hash and the received hash, orvalues dependent thereon. The server checks at 1328 whether the hashesare consistent. If the hashes are consistent, the server may determineat 1332 that the client device possesses the group shared secretgss_(Ci) that it has identified. If the server determines at 1328 thatthe hashes are not consistent, the server may determine at 1330 that theclient device does not possess the group shared secret gss_(Ci) that ithas identified.

As described with respect to the technique and methods illustrated inFIGS. 6-9, the technique and methods illustrated in FIGS. 10-13 allow aclient device to communicate its choice of group shared secret in a waythat cannot be understood by eavesdroppers. For example, while aneavesdropping device may overhear the hash H(T|gss_(Ci)) communicated bya particular client device, the eavesdropping device cannot determinethe identity of the group shared secret from which the hash wasobtained. Furthermore, since the hash communicated by each client devicechanges with each new time interval value T, it is not possible for aclient device to be tracked by the eavesdropper from one time intervalvalue T to the next.

FIG. 14 is a flowchart illustrating an example method to be performed bya server for identification and authentication of a client device.

At 1400, the server receives from a client device a message purportingto identify a group shared secret and purporting to prove the clientdevice's possession of the group shared secret that the message purportsto identity.

At 1402, the server determines whether the message identifies a groupshared secret and whether the client device from which the message wasreceived possesses the identified group shared secret. Thisdetermination may be made according to the method illustrated in FIGS.9-1 and 9-2, the method illustrated in FIGS. 13-1 and 13-2, or anysuitable variations thereof.

If the server determines at 1402 that the message does not identify agroup shared secret or that the client device does not possess the groupshared secret that the message identifies, the server may deny access toone or more services at 1404 and the method may end.

If the server determines at 1402 that the message does identify a groupshared secret and that the client device possesses the identified groupshared secret, the server may proceed to 1406.

At 1406, the server receives from the client device a purported identityof the client device. Then the server proceeds to determine at 1408whether the purported identity of the client device is legitimate.

This determination may be made according to the method illustrated inFIGS. 5-1 and 5-2 or any suitable variation thereof.

The purported identity may be received in the same message received fromthe client device at 1400, or in a different message. For example, theclient device may communicate a message containing the M hashesH(T|k_(C1)), H(T|k_(C2)), . . . , H(T|k_(CM)) calculated at 504 orportions thereof or values dependent thereon, the M hashes H(T|k_(G1)),H(T|k_(G2)), . . . , H(T|k_(GM)) calculated at 806 or portions thereofor values dependent thereon, the value r, the current time intervalvalue T, and the hash G([T]|gss_(Ci)|r) calculated at 808 or a portionthereof or value dependent thereon. Alternatively, in place of the Mhashes H(T|k_(G1)), H(T|k_(G2)), . . . , H(T|k_(GM)), the client devicemay include in the message the hash H(T|gss_(Ci)) calculated at 1206 ora portion thereof or value dependent thereon.

If the server determines at 1408 that the purported identity of theclient device is not legitimate, the server may deny access to one ormore services at 1404 and the method may end. If the server determinesat 1408 that the purported identity of the client device is legitimate,the server may proceed to authenticate the client device at 1410. Thereare numerous methods that may be used for authentication of the clientdevice.

In one example, the client device may possess a unique key k_(CLIENT)that is known to the server. The client device may perform a hash of theunique key k_(CLIENT) and the current time interval value T andcommunicate the hash to the server. The server may then verify that thereceived hash is consistent with a corresponding hash of the server'scopy of the unique key k_(CLIENT). It should be noted, however, thatthis method of authentication would be vulnerable to replay attacksduring the period that the time interval value T remains unchanged.

In another example, the client device may use public key cryptography toestablish a secure link with the server. The client device maycommunicate a session key to the server using the server's public keysigned by a private key of the client device.

In yet another example, the server may use symmetric cryptography toauthenticate a client device. Once the server determines the purportedidentity of a client device, the server may locate a unique keyk_(CLIENT). The client may communicate a session key encrypted with theunique key k_(CLIENT), and the server may use the copy of the unique keyk_(CLIENT) that it has located in order to decrypt the session key. Thesession key may be used to establish a secure tunnel.

In yet another example, the client device may communicate to the servera session key encrypted with the server's public key, such that only theserver is able to decrypt the session key.

Further details of possible authentication methods are beyond the scopeof the present discussion.

It may be desirable to include one or more parameters necessary forauthentication in a previous message communicated by the client deviceto the server. For example, an encrypted version of the unique keyk_(CLIENT) may be included in the message that purports to include anidentity of a group shared secret or an identity of a client device orboth.

If the server determines at 1412 that the client device has not beensuccessfully authenticated, the server may deny access to one or moreservices at 1404 and the method may end.

If the server determines at 1412 that the client device has beensuccessfully authenticated, the server may provide to the client deviceaccess to one or more services at 1414.

FIG. 15 is a block diagram of an example provisioning server 1500, anexample client device 1540, and an example server 1580 configured toperform the example technique illustrated in FIG. 2.

The provisioning server 1500 is an example of the server 200 when actingin a provisioning capacity. The provisioning server 1500 comprises aprocessor 1502 which is coupled to a memory 1504 and to a communicationinterface 1506 through which it is able to communicate with one or moreclient devices, such as the client device 1540. The provisioning server1500 may contain other elements which, for clarity, are not shown inFIG. 15.

The client device 1540 is an example of any one of the client devices100. The client device 1540 comprises a processor 1542 which is coupledto a memory 1544 and to a communication interface 1546. The clientdevice 1540 may contain other elements which, for clarity, are not shownin FIG. 15.

The server 1580 is an example of the server 200 when acting in areceiving capacity. The server 1580 comprises a processor 1582 which iscoupled to a memory 1584 and to a communication interface 1586. Theserver 1580 may contain other elements which, for clarity, are not shownin FIG. 15.

The communication interfaces 1506, 1546, and 1586 may be wiredcommunication interfaces or wireless communication interfaces. Forexample, the communication interfaces 1506, 1546, and 1586 may compriseany of Universal Serial Bus (USB) interfaces, Ethernet interfaces,Integrated Services Digital Network (ISDN) interfaces, DigitalSubscriber Line (DSL) interfaces, Local Area Network (LAN) interfaces,High-Definition Multimedia (HDMI) interfaces, Digital Visual Interfaces(DVIs), or Institute of Electrical and Electronics Engineers (IEEE) 1394interfaces such as i.LINK™, Lynx^(SM) or Firewire®. Alternatively, thecommunication interfaces 1606, 1546, and 1586 may be Wireless Local AreaNetwork (WLAN) interfaces, short-range wireless communication interfacessuch as Wireless Personal Area Network (WPAN) interfaces, Wireless WideArea Network (WWAN) interfaces, or Wireless Metropolitan Area Network(WMAN) interfaces.

Each of the memories 1504, 1544, and 1584 is able to store agreed-onparameters 1510. Any of the agreed-on parameters 1510 may be agreed onby two or more of the provisioning server 1500, the client device 1540and the server 1580, depending on the particular parameter. For example,such parameters may include any hash algorithms to be used to forcalculating hashes, such as the hash algorithms H and F, parametersindicative of the nature of any combination to which a hash algorithm isto be applied, parameters indicative of any additional operations to beperformed on calculated hashes to obtain hash-dependent values, andparameters indicative of which portion of any hash or hash-dependentvalue is to be stored, communicated and/or compared. Although notexplicitly shown, each of the memories 1504, 1544, and 1584 may comprisemultiple memories or storage media. For example, cryptographic data maybe stored in a different memory or storage medium than code.

The memory 1504 of the provisioning server 1500 is able to store code1508 that, when executed by processor 1502, results in the examplemethod illustrated in FIG. 3. Alternatively, the code 1508 may be storedin a different memory (not shown) than the memory 1504. In anotherexample, some portion of the example method illustrated in FIG. 3 may beperformed by application-specific integrated circuits (ASICs) or otherdedicated hardware, without involving execution of the code 1508 by theprocessor 1502. The memory 1504 may also store applications (not shown)installed in the provisioning server 1500 to be executed by theprocessor 1502.

In addition to the agreed-on parameters 1510, the memory 1504 is alsoable to store a plurality of N client-identifying keys (k₁, . . . ,k_(N)) 1512. Alternatively, the memory 1504 may store a record (notshown) of the conditions under which the client-identifying keys (k₁, .. . , k_(N)) 1512 were generated. Although not explicitly shown, thememory 1504 may optionally store the N indices (1, . . . , N) by whichthe client-identifying keys (k₁, . . . , k_(N)) 1512 are identified.

The provisioning server 1500, being responsible for assigning to eachclient device to be provisioned a unique subset of the Nclient-identifying keys 1512, may also store in the memory 1504information 1514 from which it is determinable which of the Nclient-identifying keys 1512 were assigned to which client device.Alternatively, the information 1514 may be stored on one or moredatabases (not shown) that are accessible by the provisioning server1500.

As denoted by arrow 1520, a subset of M client-identifying keys (k_(C1),. . . , k_(CM)) 1516 that were assigned by the provisioning server 1500to the client device 1540 are able to be communicated, optionally withthe corresponding indices (C1, . . . , CM) (not shown), by theprovisioning server 1500 to the client device 1540, where they may bestored in the memory 1544. While not explicitly shown, theclient-identifying keys (k_(C1), . . . , k_(CM)) 1516 may becommunicated by the provisioning server 1500 via the communicationinterface 1506 and may be received by the client device 1540 via thecommunication interface 1546, and optionally via one or moreintermediate devices.

The memory 1544 of the client device 1540 is able to store code 1548that, when executed by processor 1542, results in the example methodillustrated in FIG. 4. Alternatively, the code 1548 may be stored in adifferent memory (not shown) than the memory 1544. In another example,some portion of the example method illustrated in FIG. 4 may beperformed by ASICs or other dedicated hardware, without involvingexecution of the code 1548 by the processor 1542. The memory 1544 mayalso store applications (not shown) installed in the client device 1540to be executed by the processor 1542. Examples of such applicationsinclude data communication applications, voice communicationapplications, messaging applications, games, calculators, and the like.

The memory 1544 is able to store a current time interval value T 1550,which may be used to calculate a hash of each of the client-identifyingkeys (k_(C1), . . . , k_(CM)) 1516 received from the server, therebyobtaining M hashes H(T|k_(C1)), . . . , H(T|k_(CM)) 1552. The memory1544 may store each hash in its entirety, as shown in FIG. 15, oralternatively may store only a portion of each hash or a value dependentthereon.

As denoted by arrow 1554, a message comprising the hashes H(T|k_(C1)), .. . , H(T|k_(CM)) 1552 or portions thereof or values dependent thereonis able to be communicated by the client device 1540 to the server 1580.The server 1580 may extract the hashes 1552 or portions thereof orvalues dependent thereon from the message and store them in the memory1584. While not explicitly shown, the message comprising the hashes 1552may be sent from the client device 1540 via the communication interface1546 and may be received by the server 1580 via the communicationinterface 1586, and optionally via one or more intermediate devices.

The memory 1584 of the server 1580 is able to store the Nclient-identifying keys (k₁, . . . , k_(N)) 1512, and optionally thecorresponding N indices (1, . . . , N) (not shown). The memory 1584 isalso able to store the information 1514 from which it is determinablewhich of the N client-identifying keys were assigned to which clientdevice. The information may comprise a relevant mapping function, alookup table, an algorithm or inverse thereof, or any other informationby which the server 1580 can determine which of the client-identifyingkeys 1512 were provisioned to which client device. Alternatively, any ofthe client-identifying keys (k₁, . . . , k_(N)) 1512 and the information1514 may be stored on the one or more databases (not shown), which areaccessible to the server 1580.

The memory 1584 is able to store code 1588 that, when executed by theprocessor 1582, results in the example method illustrated in FIGS. 5-1and 5-2. Alternatively, the code 1588 may be stored in a differentmemory (not shown) than the memory 1584. In another example, someportions of the example methods illustrated in FIGS. 5-1 and 5-2 may beperformed by ASICs or other dedicated hardware, without involvingexecution of the code 1588 by the processor 1582. The memory 1584 mayalso store applications (not shown) installed in the server 1580 to beexecuted by the processor 1582.

The memory 1584 is able to store a current time interval value T 1590.The memory 1584 may optionally store one or more previous time intervalvalues T or future time interval values T or both (not shown). Thememory 1584 is able to store a table 1592 comprising hash-dependentvalues obtained from hash calculations performed on theclient-identifying keys 1512 using the current time interval value T, asdescribed previously. The memory 1584 is also able to store anassociation 1594 of each one of the hash-dependent values in the table1592 with the one of the client-identifying keys 1512 from which it wascalculated. The memory 1584 may optionally store one or more additionaltables (not shown) of hash-dependent values and associations (not shown)determined from one or more previous time interval values T or futuretime interval values T or both.

FIG. 16 is a block diagram of an example provisioning server 1600, anexample client device 1640, and an example server 1680 configured toperform the example technique illustrated in FIG. 6.

The provisioning server 1600 is an example of the server 600 when actingin a provisioning capacity. The provisioning server 1600 comprises aprocessor 1602 which is coupled to a memory 1604 and to a communicationinterface 1606 through which it is able to communicate with one or moreclient devices, such as the client device 1640. The provisioning server1600 may contain other elements which, for clarity, are not shown inFIG. 16.

The client device 1640 is an example of any one of the client devices100. The client device 1640 comprises a processor 1642 which is coupledto a memory 1644 and to a communication interface 1646. The clientdevice 1640 may contain other elements which, for clarity, are not shownin FIG. 16.

The server 1680 is an example of the server 600 when acting in areceiving capacity. The server 1680 comprises a processor 1682 which iscoupled to a memory 1684 and to a communication interface 1686. Theserver 1680 may contain other elements which, for clarity, are not shownin FIG. 16.

The communication interfaces 1606, 1646, and 1686 may be wiredcommunication interfaces or wireless communication interfaces. Forexample, the communication interfaces 1606, 1646, and 1686 may compriseany of USB interfaces, Ethernet interfaces, ISDN interfaces, DSLinterfaces, LAN interfaces, HDMI interfaces, DVIs, or IEEE 1394interfaces such as i.LINK™, Lynx^(SM) or Firewire®. Alternatively, thecommunication interfaces 1606, 1646, and 1686 may be WLAN interfaces,short-range wireless communication interfaces such as WPAN interfaces,WWAN interfaces, or WMAN interfaces.

Each of the memories 1604, 1644, and 1684 is able to store agreed-onparameters 1610. Any of the agreed-on parameters 1610 may be agreed onby two or more of the provisioning server 1600, the client device 1640and the server 1680, depending on the particular parameter. For example,such parameters may include any hash algorithms to be used forcalculating hashes, such as the hash algorithms H, G and F, parametersindicative of the nature of any combination to which a hash algorithm isto be applied, parameters indicative of any additional operations to beperformed on calculated hashes to obtain hash-dependent values, andparameters indicative of which portion of any hash or hash-dependentvalue is to be stored, communicated and/or compared. Although notexplicitly shown, each of the memories 1604, 1644, and 1684 may comprisemultiple memories or storage media. For example, cryptographic data maybe stored in a different memory or storage medium than code.

The memory 1604 of the provisioning server 1600 is able to store code1608 that, when executed by processor 1602, results in the examplemethod illustrated in FIG. 7. Alternatively, the code 1608 may be storedin a different memory (not shown) than the memory 1604. In anotherexample, some portion of the example method illustrated in FIG. 7 may beperformed by ASICs or other dedicated hardware, without involvingexecution of the code 1608 by the processor 1602. The memory 1604 mayalso store applications (not shown) installed in the provisioning server1600 to be executed by the processor 1602.

In addition to the agreed-on parameters 1610, the memory 1604 is alsoable to store a plurality of L group shared secrets (gss₁, . . . ,gss_(L)) 1612, as well as a plurality of N group shared secretidentifying keys (k₁, . . . , k_(N)) 1616. Alternatively, the memory1604 may store records (not shown) of the conditions under which thegroup shared secrets (gss₁, . . . , gss_(L)) 1612 and/or the groupshared secret identifying keys (k₁, . . . , k_(N)) 1614 were generated.Although not explicitly shown, the memory 1604 may optionally store theL indices (1, . . . , L) by which the group shared secrets 1612 areidentified and/or the N indices (1, . . . , N) by which the group sharedsecret identifying keys (k₁, . . . , k_(N)) 1614 are identified.

The provisioning server 1600, being responsible for assigning to eachgroup shared secret a unique subset of the N group shared secretidentifying keys, also stores in the memory 1604 information 1616 fromwhich it is determinable which of the N group shared secret identifyingkeys were assigned to which of the group shared secrets 1612.

Alternatively (not shown), any of the group shared secrets (gss₁, . . ., gss_(L)) 1612, the group shared secret identifying keys (k₁, . . . ,k_(N)) 1614, and the information 1616 may be stored on one or moredatabases (not shown) that are accessible by the provisioning server1600.

As denoted by arrow 1622, a subset of P group shared secrets (gss_(C1),. . . , gss_(CP)) 1618 that were assigned by the provisioning server1600 to the client device 1640 are able to be communicated, optionallywith the corresponding indices (C1, . . . , CP) (not shown), by theprovisioning server 1600 to the client device 1640. For each of the Pgroup shared secrets 1618, the provisioning server 1600 is also able tocommunicate the group shared secret identifying keys (k_(G1), . . . ,k_(GM)) that were assigned to that group shared secret. This is denotedin FIG. 16 as the group shared secret identifying keys (k_(G1), . . . ,k_(GM))×P 1620. While not explicitly shown, the group shared secrets(gss_(C)1, . . . , gss_(CP)) 1618 and the group shared secretidentifying keys (k_(G1), . . . , k_(GM))×P 1620 may be communicated bythe provisioning server 1600 via the communication interface 1606 andmay be received by the client device 1640 via the communicationinterface 1646, and optionally via one or more intermediate devices. Theclient device 1640 may store these received values in the memory 1644.

The memory 1644 of the client device 1640 is able to store code 1648that, when executed by processor 1642, results in the example methodillustrated in FIG. 8. Alternatively, the code 1648 may be stored in adifferent memory (not shown) than the memory 1644. In another example,some portion of the example method illustrated in FIG. 8 may beperformed by ASICs or other dedicated hardware, without involvingexecution of the code 1648 by the processor 1642. The memory 1644 mayalso store applications (not shown) installed in the client device 1640to be executed by the processor 1642.

The memory 1644 is able to store a current time interval value T 1650,which it may use to calculate a hash of each of the group shared secretidentifying keys (k_(G1), . . . , k_(GM)) 1652 that correspond to agroup shared secret gss_(Ci) that it has selected from the receivedgroup shared secrets (gss_(C1), . . . , gss_(CP)) 1618 to communicate tothe server 1680. From these hash calculations, the client device 1640 isable to obtain M hashes H(T|k_(G1)), . . . , H(T|k_(GM)) 1652. Theclient device 1640 may store each hash in its entirety, as shown in FIG.16, or alternatively may store only a portion of each hash or a valuedependent thereon.

The memory 1644 is also able to store a value r 1656. The current timeinterval value T 1650 (optionally), the value r 1656 and the selectedgroup shared secret gss_(Ci) are used to obtain the hashG([T]|r|gss_(Ci)) 1654. The memory 1644 may store the hash in itsentirety, as shown in FIG. 16, or alternatively may store only a portionof the hash or a value dependent thereon.

As denoted by arrow 1658, a message comprising the hashes 1652 orportions thereof or values dependent thereon, as well as the hash 1654or portion thereof or value dependent thereon, and the value r 1656 andoptionally the time interval value T 1650 is able to be communicated bythe client device 1640 to the server 1680. The server 1680 may extractthe hashes 1652 or portions thereof or values dependent thereon, thehash 1654 or portion thereof or value dependent thereon, the value r1656 and optionally the time interval value T 1650 from the message andstore them in the memory 1684. While not explicitly shown, the messagemay be sent from the client device 1640 via the communication interface1646 and may be received by the server 1680 via the communicationinterface 1686, and optionally via one or more intermediate devices.

The memory 1684 of the server 1680 is able to store the L group sharedsecrets (gss₁, . . . , gss_(L)) 1612 as well as the N group sharedsecret identifying keys (k₁, . . . , k_(N)) 1616, and optionally theindices (1, . . . , L) and/or the indices (1, . . . , N). The memory1684 is also able to store the information 1620 from which it isdeterminable which of the N group shared secret identifying keys wereassigned to which of the group shared secrets 1612. The information maycomprise a relevant mapping function, a lookup table, an algorithm orinverse thereof, or any other information by which the server 1680 candetermine which of the group shared secret identifying keys 1612 wereassigned to which group shared secret. Alternatively, any of the groupshared secrets (gss₁, . . . , gss_(L)) 1612, the group shared secretidentifying keys (k₁, . . . , k_(N)) 1614, and the information 1620 maybe stored on the one or more databases (not shown), which are accessibleto the server 1680.

The memory 1684 is able to store code 1688 that, when executed by theprocessor 1682, results in the example method illustrated in FIGS. 9-1and 9-2. Alternatively, the code 1688 may be stored in a differentmemory (not shown) than the memory 1684. In another example, someportions of the example methods illustrated in FIGS. 9-1 and 9-2 may beperformed by ASICs or other dedicated hardware, without involvingexecution of the code 1688 by the processor 1682. The memory 1684 mayalso store applications (not shown) installed in the server 1680 to beexecuted by the processor 1682.

The memory 1684 is able to store a current time interval value T 1690.The memory 1684 may optionally store one or more previous time intervalvalues T or future time interval values T or both (not shown). Thememory 1684 is able to store a table 1692 comprising hash-dependentvalues obtained from hash calculations performed on the group sharedsecret identifying keys 1616 using the current time interval value T, asdescribed previously. The memory 1684 is also able to store anassociation 1694 of each one of the hash-dependent values in the table1692 with the one of the group shared secret identifying keys 1614 fromwhich it was calculated. The memory 1684 may optionally store one ormore additional tables (not shown) of hash-dependent values andassociations (not shown) determined from one or more previous timeinterval values T or future time interval values T or both.

FIG. 17 is a block diagram of an example provisioning server 1700, anexample client device 1740, and an example server 1780 configured toperform the example technique illustrated in FIG. 10.

The provisioning server 1700 is an example of the server 1000 whenacting in a provisioning capacity. The provisioning server 1700comprises a processor 1702 which is coupled to a memory 1704 and to acommunication interface 1706 through which it is able to communicatewith one or more client devices, such as the client device 1740. Theprovisioning server 1700 may contain other elements which, for clarity,are not shown in FIG. 17.

The client device 1740 is an example of any one of the client devices100. The client device 1740 comprises a processor 1742 which is coupledto a memory 1744 and to a communication interface 1746. The clientdevice 1740 may contain other elements which, for clarity, are not shownin FIG. 17.

The server 1780 is an example of the server 1000 when acting in areceiving capacity. The server 1780 comprises a processor 1782 which iscoupled to a memory 1784 and to a communication interface 1786. Theserver 1780 may contain other elements which, for clarity, are not shownin FIG. 17.

The communication interfaces 1706, 1746, and 1786 may be wiredcommunication interfaces or wireless communication interfaces. Forexample, the communication interfaces 1706, 1746, and 1786 may compriseany of USB interfaces, Ethernet interfaces, ISDN interfaces, DSLinterfaces, LAN interfaces, HDMI interfaces, DVIs, or IEEE 1394interfaces such as i.LINK™, Lynx^(SM) or Firewire®. Alternatively, thecommunication interfaces 1706, 1746, and 1786 may be WLAN interfaces,short-range wireless communication interfaces such as WPAN interfaces,WWAN interfaces, or WMAN interfaces.

Each of the memories 1704, 1744, and 1784 is able to store agreed-onparameters 1710. Any of the agreed-on parameters 1710 may be agreed onby two or more of the provisioning server 1700, the client device 1740and the server 1780, depending on the particular parameter. For examplesuch parameters may include any hash algorithms to be used forcalculating hashes, such as the hash algorithms H, G and F, parametersindicative of the nature of any combination to which a hash algorithm isto be applied, parameters indicative of any additional operations to beperformed on calculated hashes to obtain hash-dependent values, andparameters indicative of which portion of any hash or hash-dependentvalue is to be stored, communicated and/or compared. Although notexplicitly shown, each of the memories 1704, 1744, and 1784 may comprisemultiple memories or storage media. For example, cryptographic data maybe stored in a different memory or storage medium than code.

The memory 1704 of the provisioning server 1700 is able to store code1708 that, when executed by processor 1702, results in the examplemethod illustrated in FIG. 11. Alternatively, the code 1708 may bestored in a different memory (not shown) than the memory 1704. Inanother example, some portion of the example method illustrated in FIG.11 may be performed by ASICs or other dedicated hardware, withoutinvolving execution of the code 1708 by the processor 1702. The memory1704 may also store applications (not shown) installed in theprovisioning server 1700 to be executed by the processor 1702.

In addition to the agreed-on parameters 1710, the memory 1704 is alsoable to store a plurality of L group shared secrets (gss₁, . . . ,gss_(L)) 1712. Alternatively (not shown), any of the group sharedsecrets (gss₁, . . . , gss_(L)) 1712 may be stored on one or moredatabases (not shown) that are accessible by the provisioning server1700.

Alternatively, the memory 1704 may store records (not shown) of theconditions under which the group shared secrets (gss₁, . . . , gss_(L))1712 were generated. Although not explicitly shown, the memory 1704 mayoptionally store the L indices (1, . . . , L) by which the group sharedsecrets 1712 are identified.

As denoted by arrow 1716, a subset of P group shared secrets (gss_(C1),. . . , gss_(CP)) 1714 that were assigned by the provisioning server1700 to the client device 1740 are able to communicated, optionally withthe corresponding indices (C1, . . . , CP) (not shown), by theprovisioning server 1700 to the client device 1740. While not explicitlyshown, the group shared secrets (gss_(C1), . . . , gss_(CP)) 1714 may becommunicated by the provisioning server 1700 via the communicationinterface 1706 and may be received by the client device 1740 via thecommunication interface 1746, and optionally via one or moreintermediate devices. The client device may store these received valuesin the memory 1744.

The memory 1744 of the client device 1740 is able to store code 1748that, when executed by processor 1742, results in the example methodillustrated in FIG. 12. Alternatively, the code 1748 may be stored in adifferent memory (not shown) than the memory 1744. In another example,some portion of the example method illustrated in FIG. 12 may beperformed by ASICs or other dedicated hardware, without involvingexecution of the code 1748 by the processor 1742. The memory 1744 mayalso store applications (not shown) installed in the client device 1740to be executed by the processor 1742. Examples of such applicationsinclude data communication applications, voice communicationapplications, messaging applications, games, calculators, and the like.

The memory 1744 is able to store a current time interval value T 1750,which it may use to calculate a hash of a group shared secret gss_(Ci)that it has selected from the received group shared secrets (gss_(C1), .. . , gss_(CP)) 1714. From this calculation, the client device 1740 isable to obtain a hash H(T|gss_(Ci)) 1752. The client device 1740 maystore the hash in its entirety, as shown in FIG. 17, or alternativelymay store only a portion of the hash or a value dependent thereon.

The memory 1744 is also able to store a value r 1756. The current timeinterval value T 1750 (optionally), the value r 1756 and the selectedgroup shared secret gss_(Ci) are used to obtain the hash valueH([T]|r|gss_(Ci)) 1754. The memory 1744 may store the hash in itsentirety, as shown in FIG. 17, or alternatively may store only a portionof the hash or a value dependent thereon.

As denoted by arrow 1758, a message comprising the hash 1752 or aportion thereof or value dependent thereon, as well as the hash 1754 orportion thereof or value dependent thereon, and the value r 1756 andoptionally the time interval value T 1750 is able to be communicated bythe client device 1740 to the server 1780. The server 1780 may extractthe hash 1752 or portion thereof or value dependent thereon, the hash1754 or portion thereof or value dependent thereon, the value r 1756 andoptionally the time interval value T 1750 from the message and storethem in the memory 1784. While not explicitly shown, the message may besent from the client device 1740 via the communication interface 1746and may be received by the server 1780 via the communication interface1786, and optionally via one or more intermediate devices.

The memory 1784 of the server 1780 is able to store the L group sharedsecrets (gss₁, . . . , gss_(L)) 1712, and optionally the indices (1, . .. , L).

The memory 1784 is able to store code 1788 that, when executed by theprocessor 1782, results in the example method illustrated in FIGS. 13-1and 13-2. Alternatively, the code 1788 may be stored in a differentmemory (not shown) than the memory 1784. In another example, someportions of the example methods illustrated in FIGS. 13-1 and 13-2 maybe performed by ASICs or other dedicated hardware, without involvingexecution of the code 1788 by the processor 1782. The memory 1784 mayalso store applications (not shown) installed in the server 1780 to beexecuted by the processor 1782.

The memory 1784 is able to store a current time interval value T 1790.The memory 1784 may optionally store one or more previous time intervalvalues T or future time interval values T or both (not shown). Thememory 1784 is able to store a table 1792 comprising hash-dependentvalues obtained from hash calculations performed on the group sharedsecrets 1714 using the current time interval value T, as describedpreviously. The memory 1784 is also able to store an association 1794 ofeach one of the hash-dependent values in the table 1792 with the one ofthe group shared secret 1712 from which it was calculated. The memory1784 may optionally store one or more additional tables (not shown) ofhash-dependent values and associations (not shown) determined from oneor more previous time interval values T or future time interval values Tor both.

What is claimed is:
 1. A method to be performed by a server, the methodcomprising: storing information from which it is determinable whichunique subset of M_(q) of N group shared secret identifying keys wasassigned to each of L group shared secrets {gss_(q)}, where L, N, andM_(q) are positive integers and M_(q) is less than N; when there is achange in a modulating value: calculating for each of the N group sharedsecret identifying keys a hash of a combination comprising the groupshared secret identifying key and the modulating value; determining ahash-dependent value for each hash; and associating each hash-dependentvalue with the group shared secret identifying key from which thecorresponding hash was calculated or with an index of the group sharedsecret identifying key from which the corresponding hash was calculated;receiving a message purporting to identify one of the L group sharedsecrets {gss_(q)}; and determining whether the message identifies one ofthe L group shared secrets {gss_(q)}.
 2. The method as claimed in claim1, wherein determining whether the message identifies one of the groupshared secrets {gss_(q)} comprises: extracting from the message M_(q)components, each of the M_(q) components purporting to be ahash-dependent value determined from a hash of a combination comprisingone of the group shared secret identifying keys and a current instanceof the modulating value; determining for each of the M_(q) componentswhether the component is consistent with any of the hash-dependentvalues; where each of the M_(q) components is consistent with one of thehash-dependent values, using the association to determine the groupshared secret identifying key that is associated with the consistenthash-dependent value; using the stored information to determine whetherthe group shared secret identifying keys associated with the consistenthash-dependent values correspond to any of the unique subsets of groupshared secret identifying keys that were assigned to the L group sharedsecrets {gss_(q)}; and where the group shared secret identifying keyscorrespond to one of the unique subsets of client-identifying keys thatwas assigned to a particular one of the group shared secrets {gss_(q)},determining that the message identifies the particular one of the groupshared secrets {gss_(q)}.
 3. The method as claimed in claim 2, whereindetermining whether the component is consistent with any of thehash-dependent values comprises determining whether a portion of thecomponent is consistent with a corresponding portion of any of thehash-dependent values.
 4. The method as claimed in claim 1, furthercomprising: determining whether the message was received from a clientdevice that possesses the particular one of the group shared secrets{gss_(q)}.
 5. The method as claimed in claim 4, wherein determiningwhether the message was received from a client device that possesses theparticular one of the group shared secrets {gss_(q)} comprises:extracting from the message a value purporting to be a value r and avalue purporting to be a hash of a combination comprising the particularone of the group shared secrets {gss_(q)} and the value r, wherein r isa positive integer; calculating a hash of a combination comprising theparticular one of the group shared secrets {gss_(q)} and the extractedvalue purporting to be the value r; comparing the calculated hash of thecombination to the extracted value purporting to be the hash of thecombination; and where the values are consistent with one another,determining that the message was received from a client device thatpossesses the particular one of the group shared secrets {gss_(q)}.
 6. Amethod to be performed by a server, the method comprising: when there isa change in a modulating value: calculating for each of L group sharedsecrets {gss_(q)} a hash of a combination comprising the group sharedsecret gss_(q) and the modulating value, wherein L is a positiveinteger; determining a hash-dependent value for each hash; andassociating each hash-dependent value with the group shared secret fromwhich the corresponding hash was calculated or with an index of thegroup shared secret from which the corresponding hash was calculated;receiving a message purporting to identify a particular one of the Lgroup shared secrets {gss_(q)}; and determining whether the messageidentifies the particular one of the group shared secrets {gss_(q)}. 7.The method as claimed in claim 6, wherein determining whether themessage identifies the particular one of the group shared secrets{gss_(q)} comprises: extracting from the message a value purporting tobe a hash-dependent value determined from a hash of a combinationcomprising the particular one of the group shared secrets {gss_(q)} anda current instance of the modulating value; determining whether theextracted value is consistent with any of the hash-dependent values;where the extracted value is consistent with one of the hash-dependentvalues, using the association to determine the group shared secret thatis associated with the consistent hash-dependent value.
 8. A servercomprising: a communication interface through which the server is ableto receive a message purporting to identify a particular group sharedsecret from L group shared secrets {gss_(q)}; and a memory storinginformation from which it is determinable which unique subset of M_(q)of N group shared secret identifying keys was assigned to each of the Lgroup shared secrets {gss_(q)}, wherein the server, when there is achange in a modulating value, is operative: to calculate for each of theN group shared secret identifying keys a hash of a combinationcomprising the group shared secret identifying key and the modulatingvalue; to determine a hash-dependent value for each hash; and toassociate each hash-dependent value with the group shared secretidentifying key from which the corresponding hash was calculated or anindex of the group shared secret identifying key from which thecorresponding hash was calculated; wherein the server is furtheroperative to determine whether the message identifies one of the L groupshared secrets {gss_(q)}, and wherein L, N, and M_(q) are positiveintegers and M_(q) is less than N.
 9. The server as claimed in claim 8,wherein determining whether the message identifies the particular one ofthe group shared secrets {gss_(q)} comprises: extracting from themessage M_(q) components, each of the M_(q) components purporting to bea hash-dependent value determined from a hash of a combinationcomprising one of the group shared secret identifying keys and a currentinstance of the modulating value; determining for each of the M_(q)components whether the component is consistent with any of thehash-dependent values; where each of the M_(q) components is consistentwith one of the hash-dependent values, using the association todetermine the group shared secret identifying key that is associatedwith the consistent hash-dependent value; using the information todetermine whether the group shared secret identifying keys associatedwith the consistent hash-dependent values correspond to any of theunique subsets of group shared secret identifying keys that wereassigned to the L group shared secrets {gss_(q)}; and where the groupshared secret identifying keys correspond to one of the unique subsetsof client-identifying keys that was assigned to a particular one of thegroup shared secrets {gss_(q)}, determining that the message identifiesthe particular one of the group shared secrets {gss_(q)}.
 10. The serveras claimed in claim 9, wherein determining whether the component isconsistent with any of the hash-dependent values comprises determiningwhether a portion of the component is consistent with a correspondingportion of any of the hash-dependent values.
 11. The server as claimedin claim 8, wherein the server is further operative to determine whetherthe message was received from a client device that possesses theparticular one of the group shared secrets {gss_(q)}.
 12. The server asclaimed in claim 11, wherein determining whether the message wasreceived from a client device that possesses the particular one of thegroup shared secrets {gss_(q)} comprises: extracting from the message avalue purporting to be a value r and a value purporting to be a hash ofa combination comprising the one of the particular group shared secrets{gss_(q)} and the value r, wherein r is a positive integer; calculatinga hash of a combination comprising the particular one of the groupshared secrets {gss_(q)} and the extracted value purporting to be thevalue r; comparing the calculated hash of the combination to theextracted value purporting to be the hash of the combination; and wherethe values are consistent with one another, determining that the messagewas received from a client device that possesses the particular one ofthe group shared secrets {gss_(q)}.
 13. A server comprising: acommunication interface through which the server is able to receive amessage purporting to identify a particular one of L group sharedsecrets {gss_(q)}, wherein L is a positive integer; wherein the server,when there is a change in a modulating value, is operative: to calculatefor each of the L group shared secrets {gss_(q)} a hash of a combinationcomprising the group shared secret gss_(q) and the modulating value; todetermine a hash-dependent value for each hash; and to associate eachhash-dependent value with the group shared secret from which thecorresponding hash was calculated or with an index of the group sharedsecret from which the corresponding hash was calculated; wherein theserver is further operative to determine whether the message identifiesthe particular one of the L group shared secrets {gss_(q)}.
 14. Theserver as claimed in claim 13, wherein determining whether the messageidentifies the particular one of the group shared secrets {gss_(q)}comprises: extracting from the message a value purporting to be ahash-dependent value determined from a hash of a combination comprisingthe particular one of the group shared secrets and a current instance ofthe modulating value; determining whether the extracted value isconsistent with any of the hash-dependent values; where the extractedvalue is consistent with one of the hash-dependent values, using theassociation to determine the group shared secret that is associated withthe consistent hash-dependent value.
 15. A non-transitorycomputer-readable medium storing information from which it isdeterminable which unique subset of M_(q) of N group shared secretidentifying keys was assigned to each of L group shared secrets{gss_(q)}, the computer-readable medium further storing code which, whenexecuted by a processor of a server, causes the server, when there is achange in a modulating value: to calculate for each of the N groupshared secret identifying keys a hash of a combination comprising thegroup shared secret identifying key and the modulating value; todetermine a hash-dependent value for each hash; and to associate eachhash-dependent value with the group shared secret identifying key fromwhich the corresponding hash was calculated or with an index of thegroup shared secret identifying key from which the corresponding hashwas calculated, wherein the code, when executed by the processor,further results in the server determining whether a message receivedthrough a communication interface of the server and purporting toidentify a particular group shared secret from the L group sharedsecrets {gss_(q)} identifies one of the L group shared secrets{gss_(q)}, and wherein L, N, and M_(q) are positive integers and M_(q)is less than N.
 16. A non-transitory computer-readable medium storingcode which, when executed by a processor of a server, causes the server,when there is a change in a modulating value: to calculate for each of Lgroup shared secrets {gss_(q)} a hash of a combination comprising thegroup shared secret gss_(q) and the modulating value, wherein L is apositive integer; to determine a hash-dependent value for each hash; andto associate each hash-dependent value with the group shared secret fromwhich the corresponding hash was calculated or with an index of thegroup shared secret from which the corresponding hash was calculated,wherein the code, when executed by the processor, further results in theserver determining whether a message received through a communicationinterface of the server and purporting to identify a particular one ofthe L group shared secrets {gss_(q)} identifies the particular one ofthe L group shared secrets {gss_(q)}.